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

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.

ONE-SIDED ESTIMATES AND UNIQUENESS FOR HYPERBOLIC SYSTEMS OF BALANCE LAWS

2003 ◽  
Vol 13 (04) ◽  
pp. 527-543 ◽  
Author(s):  
PAOLA GOATIN
Keyword(s):  
Hyperbolic Systems ◽  
Decay Estimates ◽  
Balance Laws ◽  
Uniqueness Of Solutions ◽  
Local Oscillation ◽  
Systems Of Balance Laws

Uniqueness of solutions of genuinely nonlinear n × n strictly hyperbolic systems of balance laws is established moving from Oleïnik-type decay estimates. As middle step, the result relies on the fulfillment of a condition which controls the local oscillation of the solution in a forward neighborhood of each point in the t–x plane.

scholarly journals Decay estimates for hyperbolic systems

2004 ◽  
Vol 33 (1) ◽  
pp. 83-113 ◽  
Author(s):  
Vladimir GEORGIEV ◽  
Sandra LUCENTE ◽  
Guido ZILIOTTI
Keyword(s):  
Hyperbolic Systems ◽  
Decay Estimates
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