Bifurcation of equilibrai for one–dimensional semilinear equation of the thermoelasticity

Abstract

In this paper, we study the bifurcation problem for the system

with Dirichlet boundary conditions u = θ = 0 at x = 0, p. Here, ? is a nonnegative real parameter, m, k are C¹⁴ functions, k is positive and m is not identically zero. The function g will be required to be C³ and satisfying a dissipative condition. We show that if , for some integer , then the global attractor A _λ for this system has some similar qualitative properties as the attractor of the parabolic equation u_t=u_xx-λg(u) with Dirichlet boundary conditions.

Keywords:

• bifurcation, thermoelasticity, attractor