FINITE-TIME BLOW-UP AND SOLVABILITY OF A WEAK SOLUTION FOR A SUPERLINEAR REACTION-DIFFUSION PROBLEM WITH INTEGRAL CONDITIONS OF THE SECOND TYPE

The focus of this work is on a class of reaction-diffusion equations: a superlinear nonlocal issue with Neumann condition modeled by the integral condition of second type. By using the Fadeo-Galarkin method to get over the complications caused by the integral condition’s existence, we are able to demonstrate the existence of the weak solution. Next, we demonstrate the uniqueness of the problem’s weak solution by using an a priori estimate. In conclusion, we examine the blow-up solution for completeness in its finite-time case.