Global existence, asymptotic behavior, and blow-up for a parabolic p-Laplacian type equation with complex interactions at the boundary

Abdelkader El Minsari; Anass Ourraoui

doi:10.24193/subbmath.2026.1.07

Authors

Abdelkader El Minsari Department of Mathematics, Mohammed First University, Faculty of Sciences, Oujda, Morocco
Anass Ourraoui Department of Mathematics, Mohammed First University, Faculty of sciences, Oujda, Morocco

DOI:

https://doi.org/10.24193/subbmath.2026.1.07

Keywords:

p-Laplacian, global existence, blow-up, boundary value problem

Abstract

In this paper, we study the initial boundary value problem involving the p-Laplacian parabolic equation \(u_t - \Delta_{p}u + \alpha\vert u \vert^{p-2}u = 0, \quad (x,t) \in \Omega \times ]0,+\infty[,\) with logarithmic boundary condition. By using the potential wells method combined with the Nehari Manifold, we establish the existence of a weak global solution. In addition, we also obtain the decay polynomial of the weak solution. Then, by virtue of the differential inequality technique, we prove that the solutions blow up in finite time under suitable initial values.

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