This article presents an analytical study on the local and global existence of the solution of diffusion - reaction problem. We show that if the solution exists locally then, it blows up in finite time. This result covers the case that the solution exists globally. We concluded that the maximum time of existence of the solution depends on the domain, the term representing the reaction in the equation and a test function defined in this job. Likewise we propose the possibility of extending the local existence to the global one using the proper solution framework.

This article presents an analytical study on the local and global existence of the solution of diffusion - reaction problem. We show that if the solution exists locally then, it blows up in finite time. This result covers the case that the solution exists globally. We concluded that the maximum time of existence of the solution depends on the domain, the term representing the reaction in the equation and a test function defined in this job. Likewise we propose the possibility of extending the local existence to the global one using the proper solution framework.