Research
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Research interests:
From a general perspective, my research is focused on theory of existence, uniqueness and regularity of solutions of nonlinear evolution PDEs, with special interest in the case of critical nonlinearities, as well as on asymptotic behavior and characterization of special solutions of such equations. Below is a list of my most significant research papers (the choice is of course subjective).
Selected research papers:
de Andrade, B.; Siracusa, G. and Viana, A. A nonlinear fractional diffusion equation: Well-posedness, comparison results, and blow-up, Journal of Mathematical Analysis and Applications, v. 505, p. 125524, 2022.
de Andrade, B.; Silva, C. and Viana, A. L^q-solvability for an equation of viscoelasticity in power type material, Zeitschrift Fur Angewandte Mathematik und Physik, v. 72, p. 1-20, 2021.
de Andrade, B.; Viana, A. Abstract Volterra integrodifferential equations with applications to parabolic models with memory. Mathematische Annalen, v. 369, p. 1131-1175, 2017.
de Andrade, B.; Carvalho, A. N.; Carvalho-Neto, P. M.; Marín-Rubio, P. Semilinear fractional differential equations: global solutions, critical nonlinearities and comparison results. Topological Methods in Nonlinear Analysis, v. 45, p. 439-468, 2015.
de Andrade, B.; Cuevas, C. S-asymptotically $\omega$-periodic and asymptotically $\omega$-periodic solutions to semilinear Cauchy problems with non dense domain. Nonlinear Analysis, v. 72, p. 3190-3208, 2010.