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Results tagged with ap.analysis-of-pdes
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user 98050
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
1
answer
94
views
Fractional reaction-diffusion with Caputo derivative
I'm interested in the following Cauchy problem for a linear diffusion equation
$$
\begin{cases}
{^C}\!D^{a}_tu(t,x) = \sigma\Delta u(t,x),\\
u(0)=u_0\in X.
\end{cases}
$$
where ${^C}\!D^{\sigma}_t$
de …
1
vote
0
answers
94
views
Time dependent reaction-diffusion semigroup
I'm interested in the following linear reaction-diffusion equation
\begin{align*}
&\partial_tu(t,x) = \sigma(t)\Delta u(t,x),\\
& u(0)=u_0\in X
\end{align*}
where $X$ is a Banach space and $\sigma(t)$ …