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- W2147153145 abstract "We study the Cauchy problem for the semilinear nonautonomous parabolic equation $u_t=mathcal{A}(t)u+psi(t,u)$ 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 a tight evolution system of measures for the evolution operator $G(t,s)$ associated to the family of time depending second order uniformly elliptic operators $mathcal{A}(t)$. Sufficient conditions for existence in the large and 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 coefficients of the operators $mathcal{A}(t)$ are allowed to be unbounded." @default.
- W2147153145 created "2016-06-24" @default.
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- W2147153145 date "2015-03-09" @default.
- W2147153145 modified "2023-09-27" @default.
- W2147153145 title "Semilinear nonautonomous parabolic equations with unbounded coefficients in the linear part" @default.
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