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

Critical behavior for a semilinear parabolic equation with forcing term depending of time and space