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Type of partial differential equation
In mathematics, a free boundary problem (FB problem) is a partial differential equation to be solved for both an unknown function u {\displaystyle u}
Free_boundary_problem
Concept in mathematics
this evolving boundary is an unknown (hyper-)surface; hence, Stefan problems are examples of free boundary problems. Analogous problems occur, for example
Stefan_problem
Class of mathematical problems
solution is usually obtained by solving the associated free-boundary problems (Stefan problems). Let Y t {\displaystyle Y_{t}} be a Lévy diffusion in
Optimal_stopping
Motivating example in mathematical study
obstacle problem is a classic motivating example in the mathematical study of variational inequalities and free boundary problems. The problem is to find
Obstacle_problem
Ability to make choices voluntarily
possibility of free will. The problem of free will has been identified in ancient Greek philosophical literature. The notion of compatibilist free will has
Free_will
Use of mathematical and statistical methods in finance
Jr. (1965). "Appendix (to Samuelson): a free boundary problem for the heat equation arising from a problem of mathematical economics". Industrial Management
Quantitative analysis (finance)
Quantitative_analysis_(finance)
Problem of solving a partial differential equation subject to prescribed boundary values
a given region that takes prescribed values on the boundary of the region. The Dirichlet problem can be solved for many PDEs, although originally it
Dirichlet_problem
Surface of revolution of a catenary
_{0}\tanh \rho _{0}=1} . It is an embedded annular solution of the free boundary problem for the area functional in the unit ball and the critical catenoid
Catenoid
Computational method for solving partial differential equations
numerical technique in the sense that the problem is discretized not only on the boundary to satisfy boundary conditions but also inside domain to satisfy
Kansa_method
Italian mathematician (1940–2020)
of variations. In 1971 he applied his mathematical methods to a free boundary problem in the filtration of liquids through porous media with applications
Claudio_Baiocchi
Topics referred to by the same term
Look up boundary in Wiktionary, the free dictionary. Boundary or Boundaries may refer to: Border, in political geography Boundaries (2016 film), a Canadian
Boundary
Argentine mathematician
regularity theory for nonlinear partial differential equations including free-boundary problems and the Monge–Ampère equation". Caffarelli has coauthored two books:
Luis_Caffarelli
Greek mathematician and physicist (born 1951)
development of shocks past the point of formation by studying a free boundary problem with singular initial conditions. Christodoulou is a recipient of
Demetrios_Christodoulou
Constraints to computational problems
Boundary conditions in fluid dynamics are the set of constraints to boundary value problems in computational fluid dynamics. These boundary conditions
Boundary conditions in fluid dynamics
Boundary_conditions_in_fluid_dynamics
Italian mathematician
dissertation, Existence and Regularity of Monotone Solutions to a Free Boundary Problem, was supervised by David Jerison. After postdoctoral research at
Daniela_De_Silva
1924–25 body setting the Ireland–Northern Ireland border
Irish Boundary Commission (Irish: Coimisiún na Teorann) met in 1924–25 to decide on the precise delineation of the border between the Irish Free State
Irish_Boundary_Commission
Oscillating boundary layer over a plate
Stokes problem also known as Stokes second problem or sometimes referred to as Stokes boundary layer or Oscillating boundary layer is a problem of determining
Stokes_problem
Canadian-American mathematician (1925–2020)
results obtained with Eugenio Calabi on the boundary-value problem for the Monge−Ampère equation, based upon boundary regularity estimates and a method of continuity
Louis_Nirenberg
UK mathematician of Belgian origin (born 1951)
Mathematically, free boundary problems are challenging because of their nonlinearity. He has developed efficient and accurate boundary integral equation
Jean-Marc_Vanden-Broeck
Italian mathematician
their solution, their phase transitions, nonlocal operators, and free boundary problems, with applications including population dynamics, quantum mechanics
Serena_Dipierro
Two-dimensional laminar boundary layer that forms on a semi-infinite plate
2f^{(3)}+f''f=0} The boundary conditions are the no-slip condition, the impermeability of the wall and the free stream velocity outside the boundary layer u ( x
Blasius_boundary_layer
French mathematician
the AMS 215, 2012 with M. Filoche, D. Jerison, S. Mayboroda: A free boundary problem for the localization of eigenfunctions, Astérisque 392, 2017, arXiv:1406
Guy_David_(mathematician)
{R} ^{3}} Bellman's lost-in-a-forest problem – find the shortest route that is guaranteed to reach the boundary of a given shape, starting at an unknown
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
German mathematician (born 1945)
University of Munich. His research deals with, among other topics, free boundary value problems for elliptic partial differential equations and hyperbolic partial
Hans_Wilhelm_Alt
Philosophical question
The problem of evil, also known as the problem of suffering, is the philosophical question of how to reconcile the existence of evil and suffering with
Problem_of_evil
Brazilian mathematician
Differential Equations (PDE). His contributions include work on free boundary problems, an original approach to the regularity of degenerate elliptic equations
Eduardo_V._Teixeira
Lowest part of the atmosphere directly influenced by contact with the planetary surface
In meteorology, the planetary boundary layer (PBL), also known as the atmospheric boundary layer (ABL) or peplosphere, is the lowest part of the atmosphere
Planetary_boundary_layer
American mathematician (born 1932)
with interests in stochastic processes, mathematical modeling, free boundary problems, and control theory. Friedman received his Ph.D. degree in 1956
Avner_Friedman
Dimensionless parameter in fluid mechanics
film behavior represents a subset of the more general class of free boundary problems. and is important in a wide range of engineering and technological
Kapitza_number
Method of solving linear partial differential equations
to accelerate boundary element problem calculations. Derivation of closed-form Green's functions is of particular interest in boundary element method
Boundary_element_method
American mathematician
mathematics at the University of Chicago, where his research focused on free boundary problems in liquid droplets and crystal growth and where he helped found
Robert_Almgren
Mathematician (born 1963)
nonlinear waves, nonlinear equations of mixed type, free boundary problems, geometric problems, and stochastic partial differential equations. His research
Gui-Qiang_Chen
Layer of fluid in the immediate vicinity of a bounding surface
known as boundary layer transition. One way of dealing with this problem is to suck the boundary layer away through a porous surface (see Boundary layer
Boundary_layer
Partial differential equations with data on two intersecting characteristics
The Goursat problem (also called the Darboux problem) is a boundary value problem for a second-order hyperbolic partial differential equation (PDE) in
Goursat_problem
American award for mathematical analysis
work on free boundary problems, vortex theory and regularity theory" 1984 Richard Melrose for "his solution of several outstanding problems in diffraction
Bôcher_Memorial_Prize
Problem in continuous-time finance
allocate their wealth between stocks and a risk-free asset so as to maximize expected utility. The problem was formulated and solved by Robert C. Merton
Merton's_portfolio_problem
American mathematician
complex systems arising in physics and biology. This has included free-boundary problems in fluids and materials science, singularity formation in partial
Michael Shelley (mathematician)
Michael_Shelley_(mathematician)
Professor of mathematics
variations and geometric measure theory, with specific emphasis on free boundary problems. She received a Laurea cum Laude in Mathematics from the University
Donatella_Danielli
Argentine-German mathematician
expertise concerns partial differential equations and particularly free boundary problems. Korten is a dual citizen of Argentina and Germany. After a licenciatura
Marianne_Korten
French mathematician
the equilibrium of a plasma in a cavity, expressed as a nonlinear free boundary problem; Korteweg–de Vries equation; Kuramoto–Sivashinsky equation; Euler
Roger_Temam
Mathematical algorithm
used mainly in order to approximate the solutions of some specific boundary value problem for partial differential equations (PDEs). The WoS method was first
Walk-on-spheres_method
Surveyed border line between U.S. states of Delaware, Maryland, and Pennsylvania
border, later became informally known as the boundary between the Southern slave states and Northern free states. This usage came to prominence during
Mason–Dixon_line
Mathematical model
solve the problem by integrating a set of partial differential equations for the whole system, thus avoiding the explicit treatment of the boundary conditions
Phase-field_model
American chemical engineer and academic
11, 2010. Ryskin, G.; L. G. Leal (1984). "Numerical Solution of Free-Boundary Problems in Fluid Mechanics. Part 1. The Finite-Difference Technique" (PDF)
L._Gary_Leal
He moved on[when?] to free and moving boundary problems. He pioneered the study of diffusion-controlled moving boundary problems in the 1970s his involvement
John_Ockendon
hypothesis Free-air gravity anomaly Free-electron laser Free-fall atomic model FreeFOAM FreeON Free body Free body diagram Free boundary problem Free convective
Index_of_physics_articles_(F)
Geographical convention
Determining the boundaries between the continents is generally a matter of geographical convention and consensus. Several slightly different conventions
Boundaries between the continents
Boundaries_between_the_continents
Numerical method for solving physical or engineering problems
solution that has a finite number of points. FEM formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates
Finite_element_method
Ethical problem in religion
The problem of Hell is a purported ethical problem in the Abrahamic religions of Christianity and Islam, in which the existence of Hell or Jahannam for
Problem_of_Hell
Catalan mathematician (born 1988)
PDE. Some of his main contributions have been in the context of free boundary problems, integro-differential equations, and the calculus of variations
Xavier_Ros-Oton
Largest mountain-free landform in Europe
of Europe – the Central and Interior Lowlands. It is the largest mountain-free landform in Europe, although a number of highlands are identified within
European_Plain
Italian mathematician (born 1958)
Parma. She is particularly interested in Kolmogorov equations and free boundary problems. Lunardi was educated at the University of Pisa, completing her
Alessandra_Lunardi
Millennium Prize Problem
The Navier–Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier–Stokes equations, a system of partial
Navier–Stokes existence and smoothness
Navier–Stokes_existence_and_smoothness
British physicist
Dynamics in 2009, for applications of the ideas of singularities to free-boundary problems such as jet breakup, drop formation, air entrainment, thin-film
Jens_G._Eggers
German mathematician (born 1963)
2007. Garcke works on nonlinear partial differential equations, free boundary problems, phase field equations, numerical analysis and geometric evolution
Harald_Garcke
Topics referred to by the same term
techniques Semantic disambiguation, the problem of resolving semantic ambiguity Sentence boundary disambiguation, the problem in natural language processing of
Disambiguation (disambiguation)
Disambiguation_(disambiguation)
Topological space that locally resembles Euclidean space
boundary is a manifold with an edge. For example, a disk (circle plus interior) is a 2-manifold with boundary the circle, a 1-manifold. The boundary of
Manifold
Philosophical problem
In philosophy of mind, the hard problem of consciousness (or simply the hard problem) is to explain how and why organisms have qualia, phenomenal consciousness
Hard_problem_of_consciousness
Void between celestial bodies
identifying a legal space above territories free from the sovereign jurisdiction of countries. This definition of the boundary to outer space became known as the
Outer_space
American mathematician
James (1963), "The initial Value problem for the Navier-Stokes equations", in Langer, Rudolph E. (ed.), Nonlinear problems. Proceedings of a symposium conducted
James_Serrin
Values set to limit a person's interactions
feelings and problems. The National Alliance on Mental Illness tells its members that establishing and maintaining values and boundaries will improve
Personal_boundaries
Elastostatics problem in linear elasticity
(1959, p. 128) himself called it problem with ambiguous boundary conditions, since there are two alternative sets of boundary conditions the solution must
Signorini_problem
Process for fairly dividing resources
valuation. Unsolved problem in computer science What is the runtime complexity of envy-free cake-cutting? More unsolved problems in computer science When
Envy-free_cake-cutting
Italian mathematical physicist
mathematical physicist specializing in fluid dynamics, including free boundary problems and compressible flow with viscosity. She was a professor of mathematical
Mariolina_Padula
for elliptic boundary value problems", Adv Comput Math 1998;9(1): 69–95. Chen W, Tanaka M, "A meshless, integration-free, and boundary-only RBF technique
Singular_boundary_method
Geographic boundaries of political entity
Borders are generally defined as geographical boundaries, imposed either by features such as oceans and terrain, or by political entities such as governments
Border
American mathematician (1904–1988)
surfaces on and analytical nature of its boundaries which is fully free or in part, free boundary problems of water wave fronts in hydrodynamics, and
Hans_Lewy
Second-order partial differential equation
interpretation of this problem is as follows: fix the temperature on the boundary of the domain according to the given specification of the boundary condition. Allow
Laplace's_equation
Unanswered question in the study of consciousness
The boundary problem is another unsolved problem in neuroscience and phenomenology that is related to the binding problem. The boundary problem is essentially
Binding_problem
Planar maps require at most four colors
regions have the same color. Adjacent means that two regions share a common boundary of non-zero length (i.e., not merely a corner where three or more regions
Four_color_theorem
1867–1903 territorial dispute between the US and UK
The Alaska boundary dispute was a territorial dispute between the United States and the British Empire over the Canada–United States border regarding Alaska
Alaska_boundary_dispute
problems such as inverse, unbounded domain, and free-boundary problems. Some techniques have been developed to cure the fictitious boundary problem in
Method of fundamental solutions
Method_of_fundamental_solutions
American mathematician
MR 0306741. Kinderlehrer, David (1978). "Variational inequalities and free boundary problems". Bull. Amer. Math. Soc. 84: 7–26. doi:10.1090/s0002-9904-1978-14397-3
David_Kinderlehrer
Free and open-source 3D CAD software
(Inventor) and IFC. FreeCAD's support for the proprietary DWG file format has been problematic due to software license compatibility problems with the GNU LibreDWG
FreeCAD
Boundary estimation in EIT is the term used in the field of electrical impedance tomography, if the inverse problem is the estimation of boundary instead
Boundary_estimation_in_EIT
Plateau in Central, South and East Asia
is a result of a continental collision or orogeny along the convergent boundary between the Indo-Australian plate and the Eurasian plate. India began drifting
Tibetan_Plateau
Analysis and solving of problems that involve fluid flows
to analyze and solve problems that involve flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid
Computational_fluid_dynamics
thickness and shape of boundary layers formed by fluid flowing along a solid surface. The defining characteristic of boundary layer flow is that at the
Boundary_layer_thickness
Geometry problem on grid points
etc. Another variation on the problem involves converting the grid into a discrete torus by using periodic boundary conditions in which the left side
No-three-in-line_problem
Problem in celestial mechanics
semimajor axis of the conic. Stated another way, Lambert's problem is the boundary value problem for the differential equation r ¨ = − μ r ^ r 2 {\displaystyle
Lambert's_problem
Problem caused by profanity filters on the Internet
The Scunthorpe problem is the unintentional blocking of online content by a spam filter, search engine or wordfilter because the text contains a string
Scunthorpe_problem
Equations modelling predator–prey cycles
by consequence, the foxes as well. This modelling problem has been called the "atto-fox problem", an atto-fox being a notional 10−18 of a fox. A density
Lotka–Volterra_equations
Metaphor for unconventional thinking
gets outside the nine-dot square (1959), and what are the actual boundaries of the problem? (1963). Norman Vincent Peale writes about this puzzle in a 1969
Thinking_outside_the_box
Mathematical study of illumination of rooms with mirrored walls
Illumination problems are a class of mathematical problems that study the illumination of rooms with mirrored walls by point light sources. The original
Illumination_problem
Type of social dilemma
turnout. The collective action problem can be understood through the analysis of game theory and the free-rider problem, which results from the provision
Collective_action_problem
Method for load calculation in construction
are chosen such that the boundary conditions for the sum of the individual problems add up to those of the original problem. Another commonly encountered
Euler–Bernoulli_beam_theory
Dog not confined to a yard or house
Romania, free-ranging urban dogs (Romanian: câini maidanezi, lit. 'wasteland dogs'; or câini comunitari, lit. 'community dogs') have been a huge problem in
Free-ranging_dog
regularity theory for nonlinear partial differential equations including free-boundary problems and the Monge–Ampère equation". He becomes the first Latin American
2023_in_Argentina
Conventional definition of the edge of space
boundary of space may be crucial for the future of spaceflight". The Verge. Retrieved April 1, 2019. Andrew G. Haley, Space Exploration: The Problems
Kármán_line
1976. This problem is an extension of Emmons problem. Emmons problem Liñán's diffusion flame theory Clarke, J. F., & Riley, N. (1976). Free convection
Clarke–Riley_diffusion_flame
Boundary between a snow-covered and snow-free surface
Climatic snow lines The climatic snow line is the boundary between a snow-covered and snow-free surface. The actual snow line may adjust seasonally, and
Snow_line
Equations describing classical electromagnetism
potentials are preferred for explicitly solving the equations as a boundary value problem, analytical mechanics, or for use in quantum mechanics. The covariant
Maxwell's_equations
Set of primitive shapes whose union equals a polygon
vertex cover problem is polynomial for tree graphs but NP-hard for general graphs, the square covering problem is linear for hole-free polygons but NP-hard
Polygon_covering
Neglecting the phase change at the free surface, the following boundary conditions apply. The free surface should be a sharp boundary separating the two fluids
Computational methods for free surface flow
Computational_methods_for_free_surface_flow
2015 two-part Japanese animated film by Taichi Ishidate
Beyond the Boundary: I'll Be Here is a 2015 two-part Japanese animated film based on the light novel series Beyond the Boundary by Nagomu Torii, consisting
Beyond the Boundary: I'll Be Here
Beyond_the_Boundary:_I'll_Be_Here
Data structure used in image rendering
solve the partial differential equations associated with typical free boundary problems that use the level set method. The CASL research group has developed
Level_set_(data_structures)
Initial estimate or framework to the solution of a mathematical problem
is an educated guess or an additional assumption made to help solve a problem, and which may later be verified to be part of the solution by its results
Ansatz
Tendency of a fluid jet to stay attached to a surface of any form
to symmetrically shaped nozzles, it presents resonance problems. Aerodynamics Airfoil Boundary layer Circulation control wing Fluid dynamics Fluid friction
Coandă_effect
Absorbing boundary condition for wave problems
Engquist–Majda absorbing boundary conditions or Lindman–Engquist–Majda absorbing boundary conditions are a hierarchy of absorbing boundary conditions for the
Engquist–Majda absorbing boundary condition
Engquist–Majda_absorbing_boundary_condition
Topics referred to by the same term
Look up demarcation in Wiktionary, the free dictionary. Demarcation is the act of creating a boundary around a place or thing. Demarcation may also refer
Demarcation
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