Quasilinear parabolic problem with variable exponent: Qualitative analysis and stabilization

2018 ◽  
Vol 20 (08) ◽  
pp. 1750065 ◽  
Author(s):  
Jacques Giacomoni ◽  
Vicenţiu Rădulescu ◽  
Guillaume Warnault
Keyword(s):  
Weak Solution ◽  
Existence And Uniqueness ◽  
Parabolic Problem ◽  
Variable Exponent ◽  
Global Behavior ◽  
Variable Exponents ◽  
Nonlinear Parabolic ◽  
Quasilinear Parabolic Problem ◽  
Quasilinear Elliptic ◽  
Quasilinear Parabolic

We discuss the existence and uniqueness of the weak solution of the following nonlinear parabolic problem: [Formula: see text] which involves a quasilinear elliptic operator of Leray–Lions type with variable exponents. Next, we discuss the global behavior of solutions and in particular the convergence to a stationary solution as [Formula: see text].

scholarly journals Weak Solutions for Nonlinear Parabolic Equations with Variable Exponents

2017 ◽  
Vol 25 (1) ◽  
pp. 55-70 ◽  
Author(s):  
Lingeshwaran Shangerganesh ◽  
Arumugam Gurusamy ◽  
Krishnan Balachandran
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Degenerate Parabolic Equation ◽  
Nonlinear Parabolic Equations ◽  
Variable Exponents ◽  
Nonlinear Parabolic ◽  
Order Degenerate ◽  
Degenerate Parabolic

Abstract In this work, we study the existence and uniqueness of weak solu- tions of fourth-order degenerate parabolic equation with variable exponent using the di erence and variation methods.

scholarly journals Existence and Uniqueness of Solutions for the p(x)-Laplacian Equation with Convection Term

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1768
Author(s):  
Bin-Sheng Wang ◽  
Gang-Ling Hou ◽  
Bin Ge
Keyword(s):  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Convection Term ◽  
Pseudomonotone Operators ◽  
Uniqueness Of Solutions ◽  
Laplacian Equation ◽  
Uniqueness Of The Solution ◽  
Gradient Based ◽  
Surjectivity Result ◽  
Quasilinear Elliptic

In this paper, we consider the existence and uniqueness of solutions for a quasilinear elliptic equation with a variable exponent and a reaction term depending on the gradient. Based on the surjectivity result for pseudomonotone operators, we prove the existence of at least one weak solution of such a problem. Furthermore, we obtain the uniqueness of the solution for the above problem under some considerations. Our results generalize and improve the existing results.

scholarly journals Existence of a solution of a Fourier nonlocal quasilinear parabolic problem

1992 ◽  
Vol 5 (1) ◽  
pp. 43-67 ◽  
Author(s):  
Ludwik Byszewski
Keyword(s):  
Heat Conduction ◽  
Classical Solution ◽  
Parabolic Problem ◽  
Classical Theorem ◽  
Existence Of A Solution ◽  
Quasilinear Parabolic Problem ◽  
Schauder’S Theorem ◽  
Quasilinear Parabolic

The aim of this paper is to give a theorem about the existence of a classical solution of a Fourier third nonlocal quasilinear parabolic problem. To prove this theorem, Schauder's theorem is used. The paper is a continuation of papers [1]-[8] and the generalizations of some results from [9]-[11]. The theorem established in this paper can be applied to describe some phenomena in the theories of diffusion and heat conduction with better effects than the analogous classical theorem about the existence of a solution of the Fourier third quasilinear parabolic problem.

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