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Systems and partial differential equations

Grant number: 19/02512-5
Support type:Research Projects - Thematic Grants
Duration: September 01, 2019 - August 31, 2024
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Marcelo da Silva Montenegro
Grantee:Marcelo da Silva Montenegro
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Pesquisadores principais:
Ademir Pastor Ferreira ; Gabriela Del Valle Planas
Assoc. researchers:Alessio Fiscella ; Anne Caroline Bronzi ; Bianca Morelli Rodolfo Calsavara ; Djairo Guedes de Figueiredo ; Mahendra Prasad Panthee ; Marcelo Martins dos Santos ; Marcia Assumpcao Guimaraes Scialom
Associated grant(s):22/05646-5 - A qualitative study of solutions to some water wave models, AV.EXT
Associated scholarship(s):21/09611-9 - Basic Mathematical fluid dynamics, BP.IC
21/04999-9 - Evolution of the radius of analyticity for dispersive equations and systems involving them, BP.PD
20/10185-1 - Local and global behaviour of solutions of dispersive equations, BP.PD
+ associated scholarships 21/05630-9 - Wave equation: weak solution and energy decay, BP.IC
21/00196-9 - Exact controllability to trajectories and approximate controllability for semilinear heat equation, BP.MS
20/14206-3 - Existence of weak solutions for a cell-fluid Navier-Stokes model with chemotaxis, BP.PD
20/14226-4 - Dispersive equations: Controllability and stabilization in periodic domains, BP.PD - associated scholarships

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)

Articles published in Agência FAPESP Newsletter about the research grant:
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Scientific publications (14)
(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)
PEREIRA, ANDRE FERREIRA E.; PLANAS, GABRIELA. Mathematical analysis of a model describing solute trapping during solidification of binary alloys. APPLICABLE ANALYSIS, . (19/02512-5)
CARDOSO, MYKAEL; GUZMAN, CARLOS M.; PASTOR, ADEMIR. Global well-posedness and critical norm concentration for inhomogeneous biharmonic NLS. MONATSHEFTE FUR MATHEMATIK, . (19/02512-5)
ZUO, JIABIN; FISCELLA, ALESSIO; BAHROUNI, ANOUAR. xistence and multiplicity results for p(.)&q(.) fractional Choquard problems with variable orde. Complex Variables and Elliptic Equations, v. 67, n. 2, . (19/02512-5, 19/23917-3)
FARKAS, CSABA; FISCELLA, ALESSIO; WINKERT, PATRICK. Singular Finsler Double Phase Problems with Nonlinear Boundary Condition. ADVANCED NONLINEAR STUDIES, v. 21, n. 4, p. 809-825, . (19/02512-5, 19/23917-3)
VIELMA LEAL, FRANCISCO J.; PASTOR, ADEMIR. TWO SIMPLE CRITERION TO OBTAIN EXACT CONTROLLABILITY AND STABILIZATION OF A LINEAR FAMILY OF DISPERSIVE PDE'S ON A PERIODIC DOMAIN. EVOLUTION EQUATIONS AND CONTROL THEORY, . (19/02512-5, 20/14226-4)
PINHEIRO, CRISTYAN; PLANAS, GABRIELA. On the alpha-Navier-Stokes-Vlasov and the alpha-Navier-Stokes-Vlasov-Fokker-Planck equations. Journal of Mathematical Physics, v. 62, n. 3, . (19/02512-5)
LOPEZ-LAZARO, HERACLIO LEDGAR; MARIN-RUBIO, PEDRO; PLANAS, GABRIELA. Pullback Attractors for Non-Newtonian Fluids with Shear Dependent Viscosity. Journal of Mathematical Fluid Mechanics, v. 23, n. 2, . (19/02512-5)
PIMENTA, MARCOS T. O.; MONTENEGRO, MARCELO. Existence of a BV solution for a mean curvature equation. Journal of Differential Equations, v. 299, p. 51-64, . (19/02512-5, 19/14330-9)
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, . (17/19752-3, 19/02512-5)
HONDA LOPES, JULIANA; PLANAS, GABRIELA. On a non-isothermal incompressible Navier-Stokes-Allen-Cahn system. MONATSHEFTE FUR MATHEMATIK, v. 195, n. 4, p. 687-715, . (19/02512-5)
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, . (17/19752-3, 19/02512-5)
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, v. 44, n. 8, . (19/02512-5)
GUZMAN, CARLOS M.; PASTOR, ADEMIR. On the inhomogeneous biharmonic nonlinear Schrodinger equation: Local, global and stability results. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 56, . (19/02512-5)
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, . (19/02512-5, 19/23917-3)

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