Global Existence and Decay Estimates of Solutions of a Parabolic–Elliptic–Parabolic System for Ion Transport Networks

2020 ◽  
Vol 75 (2) ◽  
Author(s):  
Bin Li
Keyword(s):  
Global Existence ◽  
Ion Transport ◽  
Parabolic System ◽  
Decay Estimates ◽  
Transport Networks ◽  
Estimates Of Solutions

scholarly journals Global Existence and Decay Estimates of Energy of Solutions for a New Class of p -Laplacian Heat Equations with Logarithmic Nonlinearity

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Salah Mahmoud Boulaaras ◽  
Abdelbaki Choucha ◽  
Abderrahmane Zara ◽  
Mohamed Abdalla ◽  
Bahri-Belkacem Cheri
Keyword(s):  
Global Existence ◽  
Sufficient Conditions ◽  
Research Paper ◽  
Efficient Technique ◽  
Heat Equations ◽  
Decay Estimates ◽  
Source Terms ◽  
Estimates Of Solutions ◽  
New Class ◽  
Analytical Studies

The present research paper is related to the analytical studies of p -Laplacian heat equations with respect to logarithmic nonlinearity in the source terms, where by using an efficient technique and according to some sufficient conditions, we get the global existence and decay estimates of solutions.

GLOBAL EXISTENCE AND DECAY OF SOLUTIONS FOR A QUASI-LINEAR DISSIPATIVE PLATE EQUATION

2011 ◽  
Vol 08 (03) ◽  
pp. 591-614 ◽  
Author(s):  
YONGQIN LIU ◽  
SHUICHI KAWASHIMA
Keyword(s):  
Global Existence ◽  
Linear Parabolic Equation ◽  
Decay Estimates ◽  
Plate Equation ◽  
Estimates Of Solutions ◽  
Optimal Decay ◽  
Decay Of Solutions ◽  
Spatial Dimensions ◽  
Derivatives Of ◽  
Special Time

In this paper we focus on the initial value problem of a quasi-linear dissipative plate equation with arbitrary spatial dimensions (n ≥ 1). This equation verifies the decay property of the regularity-loss type. To overcome the difficulty caused by the regularity-loss property, we employ a special time-weighted (with negative exponent) L2energy method combined with the optimal L2decay estimates of lower-order derivatives of solutions. We obtain the global existence and optimal decay estimates of solutions under smallness and enough regularity assumptions on the initial data. Moreover, we show that the solution can be approximated by a simple-looking function, which is the fundamental solution of the corresponding fourth-order linear parabolic equation.

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.

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