scholarly journals Extinction and Decay Estimates of Solutions for thep-Laplacian Equations with Nonlinear Absorptions and Nonlocal Sources

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Xiulan Wu ◽  
Jun Fu
Keyword(s):  
Sufficient Conditions ◽  
Decay Estimates ◽  
Nonlocal Sources ◽  
Estimates Of Solutions ◽  
Nirenberg Inequality ◽  
Nonlinear Absorptions ◽  
Laplacian Equations

We investigate the extinction and decay estimates of thep-Laplacian equations with nonlinear absorptions and nonlocal sources. By Gagliardo-Nirenberg inequality, we obtain the sufficient conditions of extinction solutions, and we also give the precise decay estimates of the extinction 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.

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.

Decay estimates of solutions for a hybrid system of flexible structures

1993 ◽  
Vol 4 (3) ◽  
pp. 303-319 ◽  
Author(s):  
Bopeng Rao
Keyword(s):  
Rigid Body ◽  
Hybrid System ◽  
Flexible Structures ◽  
Decay Estimates ◽  
Uniform Decay ◽  
Estimates Of Solutions ◽  
Dissipative Boundary

We consider a hybrid system consisting of a cable linked at its end to a rigid body. It is proved that such a hybrid system can be asymptotically stabilized by means of dissipative boundary feedbacks. Uniform decay estimates of energy are also established.

DECAY ESTIMATES OF SOLUTIONS TO A SEMI-LINEAR DISSIPATIVE PLATE EQUATION

2010 ◽  
Vol 07 (03) ◽  
pp. 471-501 ◽  
Author(s):  
YOUSUKE SUGITANI ◽  
SHUICHI KAWASHIMA
Keyword(s):  
Initial Data ◽  
Sobolev Spaces ◽  
Linear Problem ◽  
Dimensional Space ◽  
Weighted Sobolev Spaces ◽  
Decay Estimates ◽  
Plate Equation ◽  
Estimates Of Solutions ◽  
Optimal Decay ◽  
Additional Regularity

We study the initial value problem for a semi-linear dissipative plate equation in n-dimensional space. We observe that the dissipative structure of the linearized equation is of the regularity-loss type. This means that we have the optimal decay estimates of solutions under the additional regularity assumption on the initial data. This regularity-loss property causes the difficulty in solving the nonlinear problem. For our semi-linear problem, this difficulty can be overcome by introducing a set of time-weighted Sobolev spaces, where the time-weights and the regularity of the Sobolev spaces are determined by our regularity-loss property. Consequently, under smallness condition on the initial data, we prove the global existence and optimal decay of the solution in the corresponding Sobolev spaces.

Decay Estimates of Solutions for Quasi-Linear Hyperbolic Systems of Viscoelasticity

2012 ◽  
Vol 44 (3) ◽  
pp. 1976-2001 ◽  
Author(s):  
Priyanjana M. N. Dharmawardane ◽  
Tohru Nakamura ◽  
Shuichi Kawashima
Keyword(s):  
Hyperbolic Systems ◽  
Decay Estimates ◽  
Estimates Of Solutions
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