Existence of Weak Solutions for a Kind of Parabolic Steklov Problems (Journal of Nonlinear Modeling and Analysis, 2025)
Our focus in this study revolves around investigating the followingparabolic problemBy using the Galerkin approximation and a family of potential wells, we obtainthe existence of global solution and finite time blow-up under some suitableconditions. On the other hand, the results for asymptotic behavior of certainsolutions with positive initial energy are also given.
Keywords: Parabolic problem; global existence; blow-up; asymptotic behavior.