Existence and nonexistence of solutions of reaction-diffusion equation with Robin boundary condition
Ukr. Mat. Zh. - 2016. - 68, № 3. - pp. 423-432
We investigate the long-time behavior of the reaction-diffusion equation, which has a nonlinearity of polynomial growth of any order, with Robin boundary condition. Sufficient conditions are obtained for the solutions of the problem to be bounded or approaching infinity at a finite time.