Bifurcation of Equilibria for One-dimensional Semilinear Equation of the Thermoelasticity

Abstract

In this paper, we study the bifurcation problem for the system [formula omitted] with Dirichlet boundary conditions u = θ = 0 at x = 0,π. Here, A is a nonnegative real parameter, m, k are C1functions, k is positive and m is not identically zero. The function g will be required to be C3and satisfying a dissipative condition. We show that if n2 < λ < (n + 1)2, for some integer n ≥ 0, then the global attractor Aλ for this system has some similar qualitative properties as the attractor of the parabolic equation ut= uxx — λg(u) with Dirichlet boundary conditions. © 1994, Taylor & Francis Group, LLC. All rights reserved.