trong solutions for semilinear problems with almost sectorial operator

Autor(es)

Belluzi, Maykel ^[1] ; Caraballo, Tomas ^[2] ; Nascimento, Marcelo J. D. ^[1] ; Schiabel, Karina ^[1]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil

^[2] Univ Seville, Dept Ecuac Diferenciales & Anal Numer, Apdo Correos 1160, Seville 41080 - Spain

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF EVOLUTION EQUATIONS; v. 22, n. 1 MAR 2022.
• Citações Web of Science: 0

Resumo

In this paper. we study a semilinear parabolic problem u(t) + Au = f(t, u), t > tau; u(tau) = u(0) is an element of X, in a Banach space X, where A : D(A) subset of X -> X is an almost sectorial operator. This problem is locally well-posed in the sense of mild solutions. By exploring properties of the semigroup of growth 1 - alpha generated by -A, we prove that the local mild solution is actually strong solution for the equation. This is done without requiring any extra regularity for the initial condition u(0) is an element of X and under suitable assumptions on the nonlinearity f . We apply the results for a reaction-diffusion equation in a domain with handle where the nonlinearity f satisfies a polynomial growth vertical bar f(t, u) - f(t, v)vertical bar <= C vertical bar u - v vertical bar(1 + vertical bar u vertical bar(rho-1) + vertical bar v vertical bar(rho-1)), and we establish values of rho for which the problem still have strong solution. (AU)

• Processo FAPESP: 19/26841-8 - Estudo de problemas semilineares parabólicos e hiperbólicos não-autônomos
• Beneficiário: Marcelo José Dias Nascimento
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 17/17502-0 - Semicontinuidades superior e inferior de atratores associados a problemas de evolução com operadores quase sectoriais
• Beneficiário: Maykel Boldrin Belluzi
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Doutorado
• Processo FAPESP: 17/09406-0 - Problemas de evolução semilineares com operadores quase setoriais
• Beneficiário: Maykel Boldrin Belluzi
• Modalidade de apoio: Bolsas no Brasil - Doutorado