scholarly journals Existence and uniqueness of weak solutions for a fourth-order nonlinear parabolic equation

2007 ◽  
Vol 325 (1) ◽  
pp. 636-654 ◽  
Author(s):  
Meng Xu ◽  
Shulin Zhou
Keyword(s):  
Parabolic Equation ◽  
Fourth Order ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Nonlinear Parabolic Equation ◽  
Nonlinear Parabolic

scholarly journals $L^{\infty }$ decay estimates of solutions of nonlinear parabolic equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hui Wang ◽  
Caisheng Chen
Keyword(s):  
Parabolic Equation ◽  
Weak Solutions ◽  
Nonlinear Parabolic Equation ◽  
Divergence Form ◽  
Decay Estimates ◽  
Laplacian Equation ◽  
Estimates Of Solutions ◽  
Nonlinear Parabolic ◽  
Doubly Nonlinear ◽  
Doubly Nonlinear Parabolic Equation

AbstractIn this paper, we are interested in $L^{\infty }$ L ∞ decay estimates of weak solutions for the doubly nonlinear parabolic equation and the degenerate evolution m-Laplacian equation not in the divergence form. By a modified Moser’s technique we obtain $L^{\infty }$ L ∞ decay estimates of weak solutiona.

scholarly journals Continuity of the temperature in a multi-phase transition problem

2021 ◽  
Author(s):  
Ugo Gianazza ◽  
Naian Liao
Keyword(s):  
Phase Transition ◽  
Parabolic Equation ◽  
Modulus Of Continuity ◽  
Weak Solutions ◽  
Nonlinear Parabolic Equation ◽  
Nonlinear Parabolic ◽  
Phase Transition Problem ◽  
Doubly Nonlinear ◽  
Doubly Nonlinear Parabolic Equation ◽  
Multi Phase

AbstractLocally bounded, local weak solutions to a doubly nonlinear parabolic equation, which models the multi-phase transition of a material, is shown to be locally continuous. Moreover, an explicit modulus of continuity is given. The effect of the p-Laplacian type diffusion is also considered.

scholarly journals Asymptotic behavior of solutions for a semibounded nonmonotone evolution equation

2003 ◽  
Vol 2003 (9) ◽  
pp. 521-538
Author(s):  
Nikos Karachalios ◽  
Nikos Stavrakakis ◽  
Pavlos Xanthopoulos
Keyword(s):  
Dynamical System ◽  
Asymptotic Behavior ◽  
Parabolic Equation ◽  
Evolution Equation ◽  
Existence And Uniqueness ◽  
Nonlinear Parabolic Equation ◽  
Evolution Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Uniqueness Of Solutions ◽  
Nonlinear Parabolic

We consider a nonlinear parabolic equation involving nonmonotone diffusion. Existence and uniqueness of solutions are obtained, employing methods for semibounded evolution equations. Also shown is the existence of a global attractor for the corresponding dynamical system.

scholarly journals A New Method to Deal with the Stability of the Weak Solutions for a Nonlinear Parabolic Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Huashui Zhan
Keyword(s):  
Parabolic Equation ◽  
Weak Solutions ◽  
Nonlinear Parabolic Equation ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
New Method ◽  
Boundary Value Condition ◽  
Partial Boundary Value Condition ◽  
Nonlinear Parabolic ◽  
The Stability

Consider the nonlinear parabolic equation ∂u/∂t-div(a(x)|∇u|p-2∇u)=f(x,t,u,∇u) with axx∈Ω>0 and a(x)x∈∂Ω=0. Though it is well known that the degeneracy of a(x) may cause the usual Dirichlet boundary value condition to be overdetermined, and only a partial boundary value condition is needed, since the nonlinearity, this partial boundary can not be depicted out by Fichera function as in the linear case. A new method is introduced in the paper; accordingly, the stability of the weak solutions can be proved independent of the boundary value condition.

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