The stationary phase method and applications to evolution partial differential equations

• Grant number: 20/08276-9
• Support Opportunities: Regular Research Grants
• Start date: September 01, 2020
• End date: August 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcelo Rempel Ebert
• Grantee: Marcelo Rempel Ebert
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil

Abstract

In this project, we are interested in the asymptotic behavior (in time) of solutions to the Cauchy problem for some evolution partial differential em espaços de funções como Lebesgue $L^p, p\geq 1$, Sobolev e Besov. We plan to apply these estimates to study semi-linear problems. In particular, we are interested in proving results about global existence (in time) of the solutions, possibly assuming small initial data. Also blow-up results and the life-span of solutions are topics of interest. (AU)

Scientific publications

(5)

(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)

D'ABBICCO, MARCELLO; EBERT, MARCELO REMPEL. L-p - L-q estimates for a parameter-dependent multiplier with oscillatory and diffusive components. Journal of Mathematical Analysis and Applications, v. 504, n. 1, DEC 1 2021. (20/08276-9)

EBERT, MARCELO; MARQUES, JORGE. Critical exponent of Fujita type for semilinear wave equations in Friedmann-Lemaitre-Robertson-Walker spacetime. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, v. N/A, p. 34-pg., 2022-08-25. (20/08276-9)

D'ABBICCO, M.; EBERT, M. R.. The critical exponent for semilinear sigma-evolution equations with a strong non-effective damping. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 215, FEB 2022. (20/08276-9)

EBERT, M. R.; REISSIG, M.. A note to semilinear de Sitter models in 1d with balanced mass and dissipation. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 71, p. 9-pg., 2023-06-01. (20/08276-9)

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)