| 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) | |
| News published in Agência FAPESP Newsletter about the scholarship: | |
| More itemsLess items | |
| TITULO | |
| Articles published in other media outlets ( ): | |
| More itemsLess items | |
| VEICULO: TITULO (DATA) | |
| VEICULO: TITULO (DATA) | |