  We investigate the large-time behavior of the sign-changing solution of the
inhomogeneous semilinear heat equation with a forcing term depending of time
and space. we identify the critical exponent for this problem, which separates
the nonexistence/existence of global-in-time solutions, and show the
discontinuity of this critical exponent at the point which the inhomogeneous
term becomes independent of time variable.

Analysis of PDEs