Critical exponent of non‐global solutions for an inhomogeneous pseudo‐parabolic equation with space‐time forcing term

Abstract

We investigate the critical exponent of non‐global solutions to the following inhomogeneous pseudo‐parabolic equation with a space‐time forcing term: where is an integer; , , and are three constants; and . By obtaining a priori estimate for the solutions and the contradiction argument, we show that there exists a critical exponent: such that the problem does not admit any global solutions when and . Our obtained results show that the forcing term induces an interesting phenomenon of continuity/discontinuity of the critical exponent depending on the dimension . Namely, we found that when , ; when ; and when , . Furthermore, with when and when coincides with the critical exponent of the above problem with .