Study of solutions to a class of certain parabolic systems with variable exponents

Abstract

In this paper, the authors study an initial and boundary value problem to a system of evolution p(x)-Laplacian systems coupled with general nonlinear terms: ai(x)uit − div(|∇ui|pi(x)−2∇ui) = fi(x, u1, u2), (i = 1, 2). The authors translate the parabolic equation into the elliptic equation by using the time discretization method, and then the existence and uniqueness solution are obtained. The blow-up results is shown, by using the energy method.

Keywords

• pi(x)-Laplacian systems
• Existence
• Uniqueness
• Variable exponent
• Blow-Up
• Semi-discretization