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Systems and partial differential equations

Abstract

The project consists of the study of central themes in partial differential equations and non-linear systems, both evolutionary and stationary. The main objective of our research are themathematical aspects of equations and systems that have great interaction with geometric pro-blems, reaction and diffusion models, phenomena in thermomechanics of continuous media andphysical-chemical behavior. We are interested in showing the existence of solutions and theirgeometric properties, regularity, uniqueness or not, stability or instability, formation of singula-rities or vortices, asymptotic behavior, approximation of solutions, well-posedeness, scatteringand dependence with respect to the initial data or any other important parameters that mayoccur in the problem. The mathematical techniques to be used rest on nonlinear analysis,variational methods, Schauder theory, approximation methods, subsolution and supersolutionmethod, Galerkin method, semigroup theory, Kato theory, among others. (AU)

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Scientific publications (6)
(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)
ZUO, JIABIN; AN, TIANQING; FISCELLA, ALESSIO. A critical Kirchhoff-type problem driven by a p (.)-fractional Laplace operator with variable s (.) -order. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, v. 44, n. 1, p. 1071-1085, JAN 15 2021. Web of Science Citations: 2.
ARAUJO, RAWLILSON O.; BOCANEGRA-RODRIGUEZ, LITO E.; CALSAVARA, BIANCA M. R.; SEMINARIO-HUERTAS, PAULO N.; SOTELO-PEJERREY, ALFREDO. Global attractors for a system of elasticity with small delays. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, JAN 2021. Web of Science Citations: 0.
GUZMAN, CARLOS M.; PASTOR, ADEMIR. On the inhomogeneous biharmonic nonlinear Schrodinger equation: Local, global and stability results. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 56, DEC 2020. Web of Science Citations: 0.
ZUO, JIABIN; FISCELLA, ALESSIO; BAHROUNI, ANOUAR. Existence and multiplicity results for p(center dot)&q(•) fractional Choquard problems with variable order. Complex Variables and Elliptic Equations, OCT 2020. Web of Science Citations: 0.
ZUO, JIABIN; AN, TIANQING; FISCELLA, ALESSIO. A critical Kirchhoff-type problem driven by a p(.)-fractional Laplace operator with variable s(.)-order. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, v. 44, n. 1 AUG 2020. Web of Science Citations: 3.
FISCELLA, ALESSIO; PUCCI, PATRIZIA. DEGENERATE KIRCHHOFF (p,q)-FRACTIONAL SYSTEMS WITH CRITICAL NONLINEARITIES. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, v. 23, n. 3, p. 723-752, JUN 2020. Web of Science Citations: 0.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.