Existence and attractivity results for a class of degenerate functional- parabolic problems
type: Item
instance of: scholarly article
title: Existence and attractivity results for a class of degenerate functional- parabolic problems
zbMATH Open document ID: 0669.35057
author: M. Badii
author: J. I. Díaz
author: Alberto Tesei
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1987-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108072
review text: We want to study existence, uniqueness and asymptotical behaviour of the solutions of the following problem: \[ \partial_ tu(t,x)=\Delta u^ m(t,x)+a(x)u(t,x)-b(x)u^ 2(t,x)- \] \[ -u(t,x)\int^{t}_{-\infty}ds k(t-s,x)u(s,x)\quad in\quad (0,\infty)\times \Omega, \] \[ u(t,x)=0\quad in\quad (0,\infty)\times \partial \Omega;\quad u(t,x)=u_ 0(t,x)\quad in\quad (-\infty,0]\times \Omega. \]
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 35R20
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 4096020
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: asymptotical behaviour
MaRDI profile type: Publication
cites work: Stabilization of solutions of a degenerate nonlinear diffusion problem
cites work: Q4171189
cites work: Existence and invariance for parabolic functional equations
cites work: Nonlinear parabolic equations involving measures as initial conditions
cites work: Semi-linear second-order elliptic equations in \(L^1\)
cites work: Attractivity properties of nonnegative solutions for a class of nonlinear degenerate parabolic problems
cites work: On the Existence of a Free Boundary for a Class of Reaction-Diffusion Systems
cites work: Invariant sets for functional differential equations in Banach spaces and applications
cites work: Functional differential equations in Banach spaces: Growth and decay of solutions.
cites work: On the diffusion of biological populations
cites work: Global bifurcation and attractivity of stationary solutions of a degenerate diffusion equation
cites work: ON THE THEORY OF UPPER AND LOWER SOLUTIONS AND THE SOLVABILITY OF QUASILINEAR INTEGRO-DIFFERENTIAL EQUATIONS
cites work: On a class of nonlinear Neumann problems of parabolic type: Blow-up of solutions
cites work: Q3795521
cites work: Q3216987
cites work: On a diffusion volterra equation
cites work: Q3913868
cites work: Monotone methods and attractivity results for Volterra integro-partial differential equations
cites work: Uniqueness in a diffusion model of population biology
cites work: On some regular multiple integral problems in the calculus of variations
cites work: Stability properties for partial Volterra integrodifferential equations
cites work: Q3916991
cites work: Q4477979
cites work: The nonlinear version of Pazy's local existence theorem
cites work: Compactness methods for an abstract nonlinear Volterra integrodifferential equation
cites work: An existence result for a class of nonlinear evolution equations in Banach spaces
cites work: On a certain class of semilinear Volterra diffusion equations
description: scientific article; zbMATH DE number 4096020