Boundary value problems | Partial differential equations
In mathematics, a free boundary problem (FB problem) is a partial differential equation to be solved for both an unknown function and an unknown domain . The segment of the boundary of which is not known at the outset of the problem is the free boundary. FBs arise in various mathematical models encompassing applications that ranges from physical to economical, financial and biological phenomena, where there is an extra effect of the medium. This effect is in general a qualitative change of the medium and hence an appearance of a phase transition: ice to water, liquid to crystal, buying to selling (assets), active to inactive (biology), blue to red (coloring games), disorganized to organized (self-organizing criticality). An interesting aspect of such a criticality is the so-called sandpile dynamic (or Internal DLA). The most classical example is the melting of ice: Given a block of ice, one can solve the heat equation given appropriate initial and boundary conditions to determine its temperature. But, if in any region the temperature is greater than the melting point of ice, this domain will be occupied by liquid water instead. The boundary formed from the ice/liquid interface is controlled dynamically by the solution of the PDE. (Wikipedia).
Xavier Ros-Oton: Regularity of free boundaries in obstacle problems, Lecture III
Free boundary problems are those described by PDE that exhibit a priori unknown (free) interfaces or boundaries. Such type of problems appear in Physics, Geometry, Probability, Biology, or Finance, and the study of solutions and free boundaries uses methods from PDE, Calculus of Variations
From playlist Hausdorff School: Trending Tools
Xavier Ros-Oton: Regularity of free boundaries in obstacle problems, Lecture II
Free boundary problems are those described by PDE that exhibit a priori unknown (free) interfaces or boundaries. Such type of problems appear in Physics, Geometry, Probability, Biology, or Finance, and the study of solutions and free boundaries uses methods from PDE, Calculus of Variations
From playlist Hausdorff School: Trending Tools
Xavier-Ros Oton: Regularity of free boundaries in obstacle problems Lecture I
Free boundary problems are those described by PDE that exhibit a priori unknown (free) interfaces or boundaries. Such type of problems appear in Physics, Geometry, Probability, Biology, or Finance, and the study of solutions and free boundaries uses methods from PDE, Calculus of Variations
From playlist Hausdorff School: Trending Tools
Xavier Ros-Oton: Regularity of free boundaries in obstacle problems, Lecture IV
Free boundary problems are those described by PDE that exhibit a priori unknown (free) interfaces or boundaries. Such type of problems appear in Physics, Geometry, Probability, Biology, or Finance, and the study of solutions and free boundaries uses methods from PDE, Calculus of Variations
From playlist Hausdorff School: Trending Tools
Boundary Value Problem (Boundary value problems for differential equations)
Boundary Value Problems are not to bad! Here's how to solve a (2 point) boundary value problem in differential equations. Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additio
From playlist Differential Equations
Lauri Oksanen: On the boundary control method
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Partial Differential Equations
Intro to Boundary Value Problems
This video introduces boundary value problems. The general solution is given. Video Library: http://mathispower4u.com
From playlist Introduction to Differential Equations
How to determine eigenvalues of a boundary value problem
How to determine the eigenvalues of a boundary value problem. A basic Sturm Liouville differential equation is discussed, subject to some boundary conditions. We determine necessary conditions for the problem to admit positive eigenvalues. We also show how to prove the problem has exact
From playlist Differential equations
Jim Nolen: "A free boundary problem from Brownian bees in the infinite swarm limit in R^d"
High Dimensional Hamilton-Jacobi PDEs 2020 Workshop IV: Stochastic Analysis Related to Hamilton-Jacobi PDEs "A free boundary problem from Brownian bees in the infinite swarm limit in R^d" Jim Nolen - Duke University Abstract: I will discuss a stochastic interacting particle system in R^d
From playlist High Dimensional Hamilton-Jacobi PDEs 2020
Sarah Penington (Bath) -- Brownian bees in the infinite swarm limit
Consider a system of N particles moving according to Brownian motions and branching at rate one. Each time a particle branches, the particle in the system furthest from the origin is killed. The large N and large time behaviour of the system is related to solutions of a novel non-linear fr
From playlist Columbia Probability Seminar
Lec 17 | MIT 18.085 Computational Science and Engineering I, Fall 2008
Lecture 17: Finite elements in 1D (part 1) License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.085 Computational Science & Engineering I, Fall 2008
Mykhaylo Shkolnikov (Princeton) -- A sharp interface limit in the Giacomin-Lebowitz model
We will discuss the segregation process of two immiscible substances (e.g., oil and water) that have been mixed together. In 1996, Giacomin and Lebowitz proposed a mathematical model for this process that can be viewed as an alternative to the celebrated Cahn-Hilliard equation. They also c
From playlist Columbia SPDE Seminar
Alessio FIGALLI - The singular set in the Stefan problem
https://ams-ems-smf2022.inviteo.fr/i
From playlist International Meeting 2022 AMS-EMS-SMF
Shi-Bing Chen (7/28/22): The optimal partial transport problem
Abstract: In the optimal partial transport problem we are asked to find the most economical way to transport a portion of mass of the source domain to the target domain. It was proved by Caffarelli and McCann that there is a $C^{1,\alpha}$ hypersurface, called free boundary, separating the
From playlist Applied Geometry for Data Sciences 2022
(4.1.1): Boundary Value Problems
This video defines a boundary value problems and then provides two examples of solving boundary value problems https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Lec 25 | MIT 18.085 Computational Science and Engineering I, Fall 2008
Lecture 25: Fast Poisson solver (part 1) License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.085 Computational Science & Engineering I, Fall 2008