# Questions tagged [semigroups-of-operators]

(Usually one-parameter) semigroups of linear operators and their applications to partial differential equations, stochastic processes such as Markov processes and other branches of mathematics.

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### Existence and uniqueness for fractional parabolic equation with transport term

Let us consider the problem \begin{equation} \begin{cases} u_t+(-\Delta)^{\sigma}u+\mathrm{div}(a(t,x)u) = 0 & \text{in } \mathbb{R}^n \times [0, T) \\ u(x,0)=u_0(x) & \text{in } \...
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### Generator of a Hilbert space valued Wiener process from the solution of a martingale problem

Let $H$ be a separable $\mathbb R$-Hilbert space, $Q\in\mathfrak L(U)$ be nonnegative and self-adjoint with $\operatorname{tr}Q<\infty$ and $(W_t)_{t\ge0}$ be a $H$-valued Wiener process on a ...
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### Uniform stability of linear operators - reference request

Let $T$ be a bounded linear operator on a complex Banach space $X$. I am looking for a reference for the following result: Theorem 1. Let $p \in [1,\infty]$. The following assertions are equivalent: (...
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### Continuity of operator exponential on subspace

Let $H$ be a separable Hilbert space with overcomplete basis $(e_t)_{t \in (0,\infty)}$ such that $\langle e_t, e_s \rangle = e^{-\vert t-s \vert}.$ We can then define the projection $P_t$ which is ...
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### $u_t=Au+F(u)$ where $A$ is the infinitesimal generator of $C_0$-semigroup

I asked this question on Mathematics Stackexchange, but got no answer. In Pavel's book: Nonlinear Evolution Operators and Semigroups - Applications to Partial Differential Equations, we have the ...