| Grant number: | 13/15140-2 |
| Support Opportunities: | Research Grants - Young Investigators Grants |
| Start date: | February 01, 2014 |
| End date: | January 31, 2016 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Analysis |
| Principal Investigator: | Marcello Dabbicco |
| Grantee: | Marcello Dabbicco |
| 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 |
| Associated researchers: | Marcelo Rempel Ebert |
| Associated scholarship(s): | 14/02713-7 - Decay estimates for semilinear hyperbolic equations, BP.JP |
Abstract
We plan to study decay estimates for linear hyperbolic equations. We are interested in different types of decay estimates in time, in Sobolev spaces. On the one hand, we will study the $L^2$ setting. On the other hand, we will study $L^p-L^q$ estimates, not necessarily on the conjugate line, distinguishing between low-frequencies and high-frequencies estimates.We plan to apply some of the derived estimates to study semilinear problems. In particular, we are interested in proving results of global existence of the solution, possibly assuming small initial data. In the case of small data solution, we will study in which cases the decay rates of the semilinear problems are the same of the linear one, and in which other cases a loss of decay appears.We plan to study both models with constant coefficients and with time-dependent coefficients. In the case of time-dependent coefficients, we will assume suitable regularity and a sufficient control on the oscillations as~$t\to\infty$, to guarantee the desired result. Also, the interaction of the time-dependent coefficients will be studied to avoid bad influence on the asymptotic profile, or to obtain better decay estimates.In a first moment, we will mainly consider wave-type equations, possibly with damping terms, and with nonlocal terms, like fractional powers of the Laplacian. We also plan to study higher order equations and possibly first-order systems, $p$-evolution equations and problems in abstract setting. (AU)
| Articles published in Agência FAPESP Newsletter about the research grant: |
| More itemsLess items |
| TITULO |
| Articles published in other media outlets ( ): |
| More itemsLess items |
| VEICULO: TITULO (DATA) |
| VEICULO: TITULO (DATA) |