Smoothing effect and asymptotic dynamics of nonautonomous parabolic equations with time-dependent linear operators

Author(s)

Belluzi, Maykel ; Caraballo, Tomas ; Nascimento, Marcelo J. D. ; Schiabel, Karina

• Document type: Journal article
• Source: Journal of Differential Equations; v. 314, p. 42-pg., 2022-01-24.

Abstract

In this paper we consider the nonautonomous semilinear parabolic problems with time-dependent linear operators u(t) + A(t)u = f (t, u), t > tau; u(tau) = u(0), in a Banach space X. Under suitable conditions, we obtain regularity results for u(t) (t, x) with respect to its spatial variable x and estimates for u(t) in stronger spaces (X-alpha). We then apply those results to a nonautonomous reaction-diffusion equation (AU)

• 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: 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: 17/09406-0 - Semilinear evolution problems with almost sectorial operators
• Grantee: Maykel Boldrin Belluzi
• Support Opportunities: Scholarships in Brazil - Doctorate