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The stationary phase method and applications to evolution partial differential equations


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)

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Scientific publications
(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, 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. Web of Science Citations: 0.
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. Web of Science Citations: 0.

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