# Questions tagged [ap.analysis-of-pdes]

Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.

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### Looking for English version of a paper of Jean Ginibre

I am in serious need of an English translation for the following paper: Séminaire Bourbaki by Jean Ginibre, Le problème de Cauchy pour des EDP semi-linéaires périodiques en variables d’espace, d'après ...
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### Can I characterize functions (in 2D), which will have compactly supported/support contained Poisson solution

I have the problem of solving Poisson equation in 2D $$\Delta u = f$$ Let's say for a moment I want to solve it on $\mathbb{R}^2$, for $f(x,y), x\in \mathbb{R}, y\in \mathbb{R}$. I know however that ...
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### Gradient of the internal energy defined on the Wasserstein space $\mathcal P_2 (\mathbb R^n)$

I'm reading the derivation of gradient of the internal energy functional defined on the Wasserstein space $\mathcal P_2 (\mathbb R^n)$ from Section 2 of Lecture 18 from the book Lectures on Optimal ...
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### Maximal regularity heat equation

Considering the heat equation on the flat torus $\mathbf{T}^d$, we have the maximal regularity estimate \begin{align*} \forall \varphi\in\mathscr{D}(\mathbf{R}\times\mathbf{T}^d),\quad \|\Delta \...
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### Pressure integrated by parts in finite element method

Most FEM texts or tutorials apply FEMs on diffusion equations where the 2nd spatial derivative is integrated by parts during weak formulation. For convection diffusion equations, there is a first ...
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