Blow-up Of Solutions In Nonlinear Multi-dimensional Thermoelasticity

In this paper we study the blow-up phenomena of weak solutions in a finite time to the following initial boundary value problem with a forcing term and a thermal memory for multi—dimensional thermoelastic model :Here by u = u(x, t) and θ = θ(x, t) we denote the displacement and the temperature difference, resperctively; Ω is a bounded domain in Rⁿ(n ≥ 1)with a smooth boundary (?)Ω ; the function f = f(t,u) is a nonautonomous forcing term ; the function g — g(t) is the relaxation kernel and the sign * denotes the convolution product , i.e. , g* y(.,t) = ∫₀^t g(t ^Τ)y(.,T)dT ; u₀(x),u₁(x),θ₀(x) denotes the initial date . we consider the problem with the kernel term g*[divK₂▽θ] ,and prove the blow—up phenomena of weak solutions in a finite time with g(t) is a positive definite kernel or with the positive kernels of the forms e^αtg(t) and e^<sup>αtg(t)(α> 0) constructed from g(t) .