Anwar A. Hussain Saleh2022-05-182022-05-185210https://drepo.sdl.edu.sa/handle/20.500.14154/2595It is known that the solution of the nonlinear reaction-diffusion equation becomes unbounded in finite time no matter how small the initial data u₀ is. This time is known as the finite blow-up time. In this thesis, we push the blow-up time into infinity for the general equation by introducing a cooling term. Also, the infinite time blow-up of u(x,t) will occur at the infinity; x = 00. R(n)enThesis