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Results tagged with ap.analysis-of-pdes
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user 18931
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
1
vote
Seeking scalar functions in n>=2 variables (preferably as solution to PDE) with limited regu...
The porous media equation
$$u_t=(u^n)_{xx}$$
has solutions with compact support and therefore is a de facto example. Regularity at the edge of the support depends on the value of n (which is >1).
Y …
- 151
0
votes
0
answers
113
views
Reference Search for a Functional Minimization Problem
Let $u(x) \ge 0$ be a non-negative, piecewise-differentiable function on the real line. Moreover, let $u(x)$ be integrable with fixed positive mass, that is
$$M \equiv\int_{x=-\infty}^\infty u(x) ~ d …
- 151