Fractional approximations of abstract semilinear parabolic problems
| Autor: | Alexandre N. Carvalho, Flank D. M. Bezerra, Marcelo J. D. Nascimento |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| Popis: | In this paper we study the abstract semilinear parabolic problem of the form \begin{document}$ \frac{du}{dt}+Au = f(u), $\end{document} as the limit of the corresponding fractional approximations \begin{document}$ \frac{du}{dt} + A^{\alpha}u = f(u), $\end{document} in a Banach space \begin{document}$ X $\end{document} , where the operator \begin{document}$ A:D(A) \subset X \to X $\end{document} is a sectorial operator in the sense of Henry [ 22 ]. Under suitable assumptions on nonlinearities \begin{document}$ f:X^\alpha\to X $\end{document} ( \begin{document}$ X^\alpha: = D(A^\alpha $\end{document} )), we prove the continuity with rate (with respect to the parameter \begin{document}$ \alpha $\end{document} ) for the global attractors (as seen in Babin and Vishik [ 4 ] Chapter 8, Theorem 2.1). As an application of our analysis we consider a fractional approximation of the strongly damped wave equations and we study the convergence with rate of solutions of such approximations. |
| Databáze: | OpenAIRE |
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