Asymptotic profiles for evolution equations with time-dependent coefficients

• Grant number: 21/01743-3
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: September 01, 2021
• End date: December 31, 2024
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcelo Rempel Ebert
• Grantee: Halit Sevki Aslan
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil
• Associated scholarship(s): 23/07827-0 - Lp-Lq decay estimates for solutions to the inviscid Boussinesq equation, BE.EP.PD

Abstract

In this project, we are interested in the asymptotic behavior (in time) of solutions for some linear and semi-linear hyperbolicequations or more in general, for evolution equations. The results are derived by developing a suitable Fourier Analysis in the phase space and by applying the well known stationary phase method. We plan to study both models with constant coefficients and with time-dependent coefficients as well. In the case of time-dependent coefficients, we will assume suitable regularity and a sufficient control of the oscillations as~$t\to\infty$. Also, we plan to apply the obtained linear estimates to prove global existence of small data solutions to associate semilinear problems with power nonlinearities. Also, in the subcritical case, to prove non-existence and blow-up results. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

ASLAN, HALIT SEVKI; EBERT, MARCELO REMPEL; REISSIG, MICHAEL. SCALE-INVARIANT SEMILINEAR DAMPED WAVE MODELS WITH MASS TERM AND INTEGRABLE IN TIME SPEED OF PROPAGATION. DIFFERENTIAL AND INTEGRAL EQUATIONS, v. 36, n. 5-6, p. 38-pg., 2023-05-01. (20/08276-9, 21/01743-3)