NONEXISTENCE OF GLOBAL SOLUTIONS FOR A SYSTEM OF SEMILINEAR PARABOLIC EQUATIONS WITH A SINGULAR POTENTIAL

We investigate the nonexistence of positive global solutions to a weakly coupled system of k second-order semilinear parabolic equations with singular potentials in a cylindrical domain, whose spatial base is the exterior of a compact set and k is an arbitrary positive integer. Depending on the weight, the degree of nonlinearity, the singularity coefficient, and the spatial dimension, we establish a Fujita-type nonexistence result. Using the test function method, we derive sufficient conditions that ensure the nonexistence of positive global solutions.