Solvability and Blow-up of Nonlinear Singular and Degenerate Problem with Nonlocal Condition

This paper addresses the blow-up behavior of a degenerate and singular nonlinear parabolic problem governed by a second-type integral condition. First, the existence and the uniqueness of solutions to this complex problem, highlighting its mathematical originality, are established. Subsequently, the conditions under which blow-up occurs within a finite time frame, a critical aspect of the study that contributes to the understanding of nonlinear dynamics in parabolic equations, is analyzed. In order to enhance the theoretical insights, various numerical approximations that illustrate the finite-time blow-up behavior of the solutions are employed. The paper provides a detailed exploration of the interplay between analytical findings and numerical simulations, offering valuable contributions to the field of nonlinear parabolic problems.