Decay estimate and non-extinction of solutions of p-Laplacian nonlocal heat equations
Sarra Toualbia, Abderrahmane Zaraï, Salah Boulaaras
Abstract
The main goal of this work is to study the initial boundary value problem of a nonlocal heat equations with logarithmic nonlinearity in a bounded domain. By using the logarithmic Sobolev inequality and potential wells method, we obtain the decay, blow-up and non-extinction of solutions under some conditions, and the results extend the results of a recent paper Lijun Yan and Zuodong Yang (2018).
Topics & Concepts
Bounded functionLaplace operatorExtinction (optical mineralogy)LogarithmDomain (mathematical analysis)Work (physics)Nonlinear systemMathematicsMathematical analysisBoundary value problemSobolev spaceHeat equationPhysicsThermodynamicsOpticsQuantum mechanicsNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringStability and Controllability of Differential Equations