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Singular solutions, symmetries and self-similarity for PDEs


In this project we will address the following kinds of nonlinear partial differential equations: Elliptic, parabolic with a singular nonlinearity, dispersive, and wave equation. We will study issues as existence of solutions without Sobolev regularity, nonradial self-similarity, invariance under certain kinds of rotations, blow-up, and asymptotic behavior. The basic strategy is to study those equations in suitable low-regularity functional spaces that allow to obtain solutions with the desired properties. (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)
FERREIRA, LUCAS C. F.; MEDEIROS, EVERALDO S.; MONTENEGRO, MARCELO. On the Laplace equation with a supercritical nonlinear Robin boundary condition in the half-space. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, v. 47, n. 3-4, p. 667-682, . (10/19098-2)
FERREIRA, LUCAS C. F.. On a bilinear estimate in weak-Morrey spaces and uniqueness for Navier-Stokes equations. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, v. 105, n. 2, p. 228-247, . (10/19098-2)

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