Nonlinear second order equations with applications to partial differential equations
type: Item
instance of: scholarly article
title: Nonlinear second order equations with applications to partial differential equations
zbMATH Open document ID: 0572.34004
DOI: 10.1016/0022-0396(85)90008-7
author: Patricio Aviles
author: James T. jun Sandefur
published in: Journal of Differential Equations
publication date: 1985-01-01T00:00:00Z
review text: In this paper we study the Cauchy problem for the abstract second order (in time) semilinear differential equation \(u''(t)+Au'(t)+Bu(t)=f(t,u(t))\) where A and B are linear operators in a Banach space. Then we use the abstract results that we obtained together with energy estimates and the center manifold theorem to study in concrete cases, global existence, stability and bifurcation of solutions of certain parabolic and hyperbolic equations.
Mathematics Subject Classification ID: 34A12
zbMATH DE Number: 3912767
zbMATH Keywords: parabolic equation
zbMATH Keywords: second order semilinear differential equation
zbMATH Keywords: Cauchy problem
zbMATH Keywords: energy estimates
zbMATH Keywords: center manifold theorem
zbMATH Keywords: global existence
zbMATH Keywords: bifurcation of solutions
zbMATH Keywords: hyperbolic equations
MaRDI profile type: Publication
full work available at URL: 0022-0396(85)90008-7
OpenAlex ID: W2050902342
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description: scientific article; zbMATH DE number 3912767