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Results tagged with linear-pde
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user 39322
Questions about linear partial differential equations. Often used in combination with the top-level tag ap.analysis-of-pdes.
10
votes
2
answers
1k
views
Well-posedness of Fokker-Planck equation
Consider the following equation on $[0,T]\times\mathbb{R}^n$
\begin{eqnarray}
&\partial_t\rho=\mathrm{div}(\rho\nabla V)+\Delta\rho\\
&\rho|_{t=0}=\rho^0,
\end{eqnarray}
where $V\in C^2(\mathbb{R}^n;\ …
- 339
6
votes
1
answer
1k
views
Regularity of solution to Fokker Planck equation
Suppose that $\rho \in L^1(\mathbb{R}^n \times (0,T))$ for every $T < \infty$ is a weak solution of the PDE
\begin{align}
\partial_t\rho &= \Delta \rho + \text{div}(\rho\nabla\Psi(x))\\
\rho(t = 0) &= …
- 339