Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations

Abstract

Abstract In this paper, we study the initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations which do not have positive energy and come from the soil mechanics, the heat conduction, and the nonlinear optics. By the mountain pass theorem we first prove the existence of nonzero weak solution to the static problem, which is the important basis of evolution problem, then based on the method of potential well we prove the existence of global weak solution to the evolution problem.

Keywords

• Nonlinear pseudo-parabolic equation
• Higher-order
• The method of potential well
• Static problem
• Existence of global weak solution