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Results tagged with ap.analysis-of-pdes
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user 9022
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
12
votes
Accepted
Use of games to approximate solutions to Partial Differential Equations
The connection between random walks, diffusion, and the heat equation is an amazing example of "the unreasonable effectiveness of mathematics." However, it's important to understand that this doesn't …
- 3,934
2
votes
Accepted
Euler-Lagrange, Gradient Descent, Heat Equation and Image Denoising
If the solution to
$
u_t=u_{xx}+u_{yy}
$
reaches an equilibrium solution, then $u_{t}=0$ at that equilibrium, so $u_{xx}+u_{yy}=0$. The author has shown that a necessary condition for $u$ to be mi …
- 3,934