Nonlinear parabolic equation having nonstandard growth condition with respect to the gradient and variable exponent
Abderrahim Charkaoui, Houda Fahim, Nour Eddine Alaa
Abstract
We are concerned with the existence of solutions to a class of quasilinear parabolic equations having critical growth nonlinearity with respect to the gradient and variable exponent. Using Schaeffer's fixed point theorem combined with the sub- and supersolution method, we prove the existence results of a weak solutions to the considered problems.
Topics & Concepts
MathematicsExponentNonlinear systemMathematical analysisClass (philosophy)Variable (mathematics)Fixed-point theoremFixed pointParabolic partial differential equationCritical exponentPartial differential equationScalingGeometryPhysicsQuantum mechanicsPhilosophyComputer scienceLinguisticsArtificial intelligenceNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNonlinear Differential Equations Analysis