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In mathematics and its applications, particularly to phase transitions in matter, a Stefan problem is a particular kind of boundary value problem for a system of partial differential equations (PDE), in which the boundary between the phases can move with time.
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.. The function is often thought of as an "unknown" that solves the equation, similar to how x is thought of as an unknown number solving, e.g., an algebraic equation like x 2 − 3x + 2 = 0.
Partial differential equation. Nonlinear partial differential equation. list of nonlinear partial differential equations; Boundary condition; Boundary value problem. Dirichlet problem, Dirichlet boundary condition; Neumann boundary condition; Stefan problem; Wiener–Hopf problem; Separation of variables; Green's function; Elliptic partial ...
The series includes the volumes Mechanics, Mechanics of Deformable Bodies, Electrodynamics, Optics, Thermodynamics and Statistical Mechanics, and Partial Differential Equations in Physics. Focusing on one subject each semester, the lectures formed a three-year cycle of courses that Sommerfeld repeatedly taught at the University of Munich for ...
The mathematical analysis of partial differential equations uses analytical techniques to study partial differential equations. The subject has connections to and motivations from physics and differential geometry, the latter through the branches of global and geometric analysis .
Bregman iteration and augmented Lagrangian type methods for L 1 and L 1-related optimization problems which are fundamental to the fields of compressed sensing, matrix completion, robust principal component analysis, etc. Overcoming the curse of dimensionality for Hamilton–Jacobi equations arising in control theory and differential games.
In mathematics, the method of characteristics is a technique for solving partial differential equations.Typically, it applies to first-order equations, though in general characteristic curves can also be found for hyperbolic and parabolic partial differential equation.
In many practical partial differential equations, one has a term that involves derivatives (such as a kinetic energy contribution), and a multiplication with a function (for example, a potential). In the spectral method, the solution is expanded in a suitable set of basis functions, for example plane waves,
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