On the solvability of some parabolic equations involving nonlinear boundary conditions with L^{1} data

Abstract

We analyze the existence of solutions for a class of quasilinear parabolic equations with critical growth nonlinearities, nonlinear boundary conditions, and \(L^1\) 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.

Keywords

• quasilinear parabolic equation
• nonlinear boundary conditions
• weak solutions
• leray-schauder topological degree
• \(l^1\)-data