Abstract
Develop research and human resources training activities in the areas of Linear Partial Differential Equations and Multidimensional Complex Analysis. (AU)
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Marcelo Rempel Ebert
CV Lattes
ResearcherID
ORCID
Universidade de São Paulo (USP). Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP) (Institutional affiliation from the last research proposal) Birthplace: Brazil
graduate at Matematica from Universidade Federal de Santa Maria (1999), master's at Mathematics from Universidade Federal de São Carlos (2001) and ph.d. at Mathematics from Universidade Federal de São Carlos (2004). Has experience in Mathematics, focusing on Partial Differential Equations, acting on the following subjects: Lp- Lq decay estimates for Evolution Operators, global existence of solution for semilinear problems. (Source: Lattes Curriculum)
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Research grants
- The critical exponent for nonlinear wave equation with structural damping, AV.EXT
Abstract
In this project, we are interested in the asymptotic behavior (in time) of solutions to the Cauchy problem for a strongly damped wave equation in Lebesgue or Sobolev spaces. 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-u…
- 14th ISAAC Congress, AO.R
- The stationary phase method and applications to evolution partial differential equations, AP.R
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, possib…
(Only some records are available in English at this moment)
Scholarships in Brazil
- Explicit abstract neutral differential equations with state-dependent delay., BP.MS
Abstract
The objective of this project is to devolop studies on the existence and uniqueness of solution for abstract neutral explicit differential equations with state-dependend delay. Our basic objective is to read the article,Hernandez, Eduardo., On Explicit Abstract Neutral Differential Equations with State-Dependent Delay II, To appear in Proc. Amer. Math. soc,on explicit neutral equati…
- Assymptotic behaviour of solutions to the Cauchy problem for systems of evolution partial differential equations, BP.PD
Abstract
In this project, we are interested in the asymptotic behavior (in time) of solutions to the Cauchy problem for semi-linear systems of evolution partial differential equations in Lebesgue Lp, Sobolev or Besov spaces. More precisely, we plan to apply the well known estimates for solutions to the associate linear problems to obtain necessay and sufficient conditions for the existence of glob…
- Asymptotic profiles for evolution equations with time-dependent coefficients, BP.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 tim…
- Fourier analysis and the asyptotic behaviors of solutions to the Cauchy problem for Partial Differential Equations, BP.IC
Abstract
In this project we are interested into study the basics in Fourier Analysis and to apply it to determine the asymptotic behavior (in time) of solutions to the Cauchy problem for some evolution partial differential in function spaces as Lebesgue spaces or Sobolev spaces.
(Only some records are available in English at this moment)
Scholarships abroad
- 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 for solutions to the Cauchy problem for the inviscid Boussinesq equation in the whole space R^n. We plan to derive long-time Lp-Lq decay estimates for solutions for time-dependent multipliers by means of the Fourier analysis and the WKB method. (AU)
- Decay estimates for hyperbolic partial differential equations in the L^p-L^q framework, BE.PQ
Abstract
In this project, we are interested in $L^p-L^q$ decay estimates (not necessarily on the conjugate line) in time for linear hyperbolic equations, probably distinguishing between estimates basing on Fourier multipliers localizing to low-frequencies and high-frequencies of the phase space. We plan to apply these estimates to study semi-linear problems. In particular, we are interested in pro…
- The Cauchy problem for a class of hyperbolic operators, BE.PQ
Abstract
In this project we are interested in discussing about necessary and sufficient conditions for the Cauchy problem so that a class ofweakly hyperbolic operators can be well-posed in spaces of functions like infinitely differentiable functions, Sobolev spaces or moreappropriate scales of function spaces. Because in the theory of weakly hyperbolic operators we have the effect of loss of…
Total / Available in English
| 1 / 1 | Ongoing grants |
| 12 / 10 | Completed research grants |
| 1 / 1 | Ongoing scholarships in Brazil |
| 7 / 6 | Completed scholarships in Brazil |
| 3 / 3 | Completed scholarships abroad |
| 24 / 21 | All research grants and scholarships |
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