trong solutions for semilinear problems with almost sectorial operator

Author(s)

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

Affiliation

^[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

• Document type: Journal article
• Source: JOURNAL OF EVOLUTION EQUATIONS; v. 22, n. 1 MAR 2022.
• Web of Science Citations: 0

Abstract

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)

• FAPESP's process: 19/26841-8 - Study of non-autonomous semilinear parabolic and hyperbolic problems
• Grantee: Marcelo José Dias Nascimento
• Support Opportunities: Regular Research Grants
• FAPESP's process: 17/17502-0 - Upper and lower semicontinuities of attractors for evolution problems with almost sectorial operators
• Grantee: Maykel Boldrin Belluzi
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• FAPESP's process: 17/09406-0 - Semilinear evolution problems with almost sectorial operators
• Grantee: Maykel Boldrin Belluzi
• Support Opportunities: Scholarships in Brazil - Doctorate