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Results tagged with ap.analysis-of-pdes
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user 129831
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
4
votes
1
answer
469
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Uniqueness of distributional solutions to the Poisson equation
Let $S(\mathbb R^n)$ denote the space of all Schwartz functions on $\mathbb R^n$ equipped with the topology induced by the usual Schwartz semi-norms. Let $S(\mathbb R^n)^*$ denote its dual.
My questio …
- 1,326
4
votes
1
answer
389
views
Decay of solutions to the wave equation $\ddot\phi(t, x)+\frac{n p}{t}\dot\phi(t,x)-t^{-2p}\...
For the physical motivation of this question, see my question 669101 on physics StackExchange.
The question is this: Let $\hat M=\mathbb R^n$ or $\hat M =(\mathbb R/\mathbb Z)^n$ for some $n\in\math …
- 1,326
3
votes
0
answers
450
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Opposite of the curl operator and Biot-Savart kernel
Note: I just realized that using $\omega$ and $w$ might not have been the smartest choice of notation -- Sorry about that.
Let $\renewcommand{\div}{\operatorname{\div}}Q_0, Q_1$ be two real numbers, $ …
- 1,326
1
vote
Decay of solutions to the wave equation $\ddot\phi(t, x)+\frac{n p}{t}\dot\phi(t,x)-t^{-2p}\...
Partial answer (the compact case for $n=3,p=2/3$ only): Let $M=\mathbb T = \mathbb R/(2\pi\mathbb Z)$ and let $\phi$ be a solution [Footnote 1] of the Klein-Gordon equation at the top of the question …
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