English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study the Cauchy problem for the semilinear nonautonomous parabolicequation $u_t=\mathcal{A}(t)u+\psi(t,u)$ in $[s,\tau]\times {{\mathbb R}^d}$,$\tau> s $, in the spaces $C_b([s, \tau]\times{{\mathbb R}^d})$ and in $L^p((s,\tau)\times{{\mathbb R}^d}, \nu)$. Here $\nu$ is a Borel measure defined via atight evolution system of measures for the evolution operator $G(t,s)$associated to the family of time depending second order uniformly ellipticoperators $\mathcal{A}(t)$. Sufficient conditions for existence in the largeand stability of the null solution are also given in both $C_b$ and $L^p$contexts. The novelty with respect to the literature is that the coefficientsof the operators $\mathcal{A}(t)$ are allowed to be unbounded.

Semilinear nonautonomous parabolic equations with unbounded coefficients in the linear part