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On the solvability of some parabolic equations involving nonlinear boundary conditions with L1 data

Taourirte Laila, Charkaoui Abderrahim, Alaa Nour Eddine

Opuscula Mathematica

2024

Vol. 44, no. 4

587--623

We analyze the existence of solutions for a class of quasilinear parabolic equations with critical growth nonlinearities, nonlinear boundary conditions, and L1 data. We formulate our problems in an abstract form, then using some techniques of functional analysis, such as Leray-Schauder’s topological degree associated with the truncation method and very interesting compactness results, we establish the existence of weak solutions to the proposed models.