Global existence, asymptotic behavior, and blow-up for a parabolic p-Laplacian type equation with complex interactions at the boundary
DOI:
https://doi.org/10.24193/subbmath.2026.1.07Keywords:
p-Laplacian, global existence, blow-up, boundary value problemAbstract
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.
Mathematics Subject Classification (2010): 35A01, 35A24, 35K20.
Received 23 June 2025; Accepted 03 February 2026.
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