All Questions
Tagged with semigroups-of-operators differential-operators
6
questions
3
votes
2
answers
134
views
Lumer-Phillips-type theorem for non-autonomous evolutions
The classical Lumer-Phillips theorem characterizes the generators of contraction semigroups. I am looking for a similar characterization or at least a sufficient condition for a family of unbounded, ...
4
votes
1
answer
144
views
approximation of a Feller semi-group with the infinitesimal generator
Let $T_t$ a Feller semigroup (see this) and let $(A,D(A))$ its infinitesimal generator.
If A is a bounded operator it is easy to show that the Feller semi-group is $e^{tA}$.
Is this formula always ...
5
votes
1
answer
157
views
Spectrum of an elliptic operator in divergence form with a reflecting boundary condition
Let $\Omega$ be a bounded open domain and $v:\Omega\to\mathbb{R}^n$. Consider the following elliptic operator in divergence form, defined on smooth functions $u: \Omega \to \mathbb{R}$
\begin{align}
L ...
1
vote
0
answers
72
views
What types of semigroups have a Laplacean type operator as infinitesimal generator?
Let $\Omega\subseteq\mathbb{R}^N$ be an open, bounded connected set having Lipschitz uniform boundary. Moreover let $d\in L^{\infty}(\Omega,\mathbb{R}^M),\ d_1(x),d_2(x),\dots, d_M(x)>d>0,\ \...
2
votes
2
answers
375
views
Why we use Caputo fractional derivative in application?
I'm working on some papers which use Caputo fractional evolution equation (see on Wikipedia) as application for thier main result:
For example:
$$\left\{\begin{matrix}
^CD^{\sigma}_tx(t)+Ax(t)=&...
1
vote
1
answer
392
views
Pullback via flow as operator group
Let $X$ be a vector field on a manifold $M$ that induces a complete flow $\Theta_t$. Then the operator family $\Theta_t^*$,
$$\Theta_t^*u(x) = u(\Theta_t(x))$$
is a strongly continuous semigroup of ...