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
• City of the host institution: Ribeirão Preto

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

(7)

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

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, 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)

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, 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)

EBERT, MARCELO REMPEL; MARQUES, JORGE; DO NASCIMENTO, WANDERLEY NUNES. The move from Fujita type exponent to a shift of it for a class of semilinear evolution equations with time-dependent damping. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, v. 31, n. 2, p. 33-pg., 2024-03-01. (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)

ASLAN, HALIT SEVKI; EBERT, MARCELO REMPEL. On the asymptotic behavior of the energy for evolution models with oscillating time-dependent damping. ASYMPTOTIC ANALYSIS, v. 135, n. 1-2, p. 23-pg., 2023-01-01. (21/01743-3, 20/08276-9)