Affiliation:
1. School of Mathematics and Statistics Southwest University Chongqing China
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
.
Funder
Natural Science Foundation of Chongqing Municipality
Subject
General Engineering,General Mathematics