scholarly journals Existence and Uniqueness of Very Singular Solution of a Degenerate Parabolic Equation with Nonlinear Convection

2009 ◽  
Vol 2009 (1) ◽  
pp. 415709
Author(s):  
ZhongBo Fang ◽  
Daxiong Piao ◽  
Jian Wang
Keyword(s):  
Parabolic Equation ◽  
Existence And Uniqueness ◽  
Singular Solution ◽  
Degenerate Parabolic Equation ◽  
Nonlinear Convection ◽  
Degenerate Parabolic ◽  
Very Singular Solution

scholarly journals Pullback Attractors for a Nonautonomous Retarded Degenerate Parabolic Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Fahe Miao ◽  
Hui Liu ◽  
Jie Xin
Keyword(s):  
Weak Solution ◽  
Parabolic Equation ◽  
Galerkin Method ◽  
Existence And Uniqueness ◽  
Degenerate Parabolic Equation ◽  
Pullback Attractors ◽  
Asymptotic Compactness ◽  
Absorbing Sets ◽  
Degenerate Parabolic ◽  
Standard Galerkin Method

This paper is devoted to a nonautonomous retarded degenerate parabolic equation. We first show the existence and uniqueness of a weak solution for the equation by using the standard Galerkin method. Then we establish the existence of pullback attractors for the equation by proving the existence of compact pullback absorbing sets and the pullback asymptotic compactness.

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.

Inverse free boundary problems for a generally degenerate parabolic equation

2015 ◽  
Vol 23 (2) ◽  
Author(s):  
Nadiya Huzyk
Keyword(s):  
Parabolic Equation ◽  
Free Boundary ◽  
Existence And Uniqueness ◽  
Degenerate Parabolic Equation ◽  
Free Boundary Problems ◽  
Time Dependent ◽  
Classical Solutions ◽  
Boundary Problems ◽  
First Derivative ◽  
Degenerate Parabolic

AbstractIn a free boundary domain we consider inverse problems for determination a time-dependent coefficient at the first derivative of an unknown function in a generally degenerate parabolic equation with different overdetermination conditions. There are established conditions of existence and uniqueness of the classical solutions to the named problems in the case of the weak degeneration.

scholarly journals On a degenerate parabolic equation with Newtonian fluid∼non-Newtonian fluid mixed type

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sujun Weng
Keyword(s):  
Parabolic Equation ◽  
Newtonian Fluid ◽  
Weak Solutions ◽  
Mixed Type ◽  
Degenerate Parabolic Equation ◽  
Type Equation ◽  
Existence Of Weak Solutions ◽  
Degenerate Parabolic ◽  
The Stability ◽  
Increasing Function

AbstractWe study the existence of weak solutions to a Newtonian fluid∼non-Newtonian fluid mixed-type equation $$ {u_{t}}= \operatorname{div} \bigl(b(x,t){ \bigl\vert {\nabla A(u)} \bigr\vert ^{p(x) - 2}}\nabla A(u)+\alpha (x,t)\nabla A(u) \bigr)+f(u,x,t). $$ u t = div ( b ( x , t ) | ∇ A ( u ) | p ( x ) − 2 ∇ A ( u ) + α ( x , t ) ∇ A ( u ) ) + f ( u , x , t ) . We assume that $A'(s)=a(s)\geq 0$ A ′ ( s ) = a ( s ) ≥ 0 , $A(s)$ A ( s ) is a strictly increasing function, $A(0)=0$ A ( 0 ) = 0 , $b(x,t)\geq 0$ b ( x , t ) ≥ 0 , and $\alpha (x,t)\geq 0$ α ( x , t ) ≥ 0 . If $$ b(x,t)=\alpha (x,t)=0,\quad (x,t)\in \partial \Omega \times [0,T], $$ b ( x , t ) = α ( x , t ) = 0 , ( x , t ) ∈ ∂ Ω × [ 0 , T ] , then we prove the stability of weak solutions without the boundary value condition.

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