scholarly journals Application of the Weighted Energy Method in the Partial Fourier Space to Linearized Viscous Conservation Laws with Non-Convex Condition

10.5772/36633 ◽  
2012 ◽  
Author(s):  
Yoshihiro Ueda
Keyword(s):  
Conservation Laws ◽  
Energy Method ◽  
Fourier Space ◽  
Weighted Energy Method ◽  
Weighted Energy ◽  
Viscous Conservation Laws ◽  
Convex Condition

Lp ENERGY METHOD FOR MULTI-DIMENSIONAL VISCOUS CONSERVATION LAWS AND APPLICATION TO THE STABILITY OF PLANAR WAVES

2004 ◽  
Vol 01 (03) ◽  
pp. 581-603 ◽  
Author(s):  
SHUICHI KAWASHIMA ◽  
SHINYA NISHIBATA ◽  
MASATAKA NISHIKAWA
Keyword(s):  
Conservation Laws ◽  
Energy Method ◽  
Optimal Convergence Rate ◽  
Estimates Of Solutions ◽  
Interpolation Inequalities ◽  
Optimal Decay ◽  
Viscous Conservation Laws ◽  
The Cauchy Problem ◽  
Whole Space ◽  
The Stability

We introduce a new Lp energy method for multi-dimensional viscous conservation laws. Our energy method is useful enough to derive the optimal decay estimates of solutions in the W1,p space for the Cauchy problem. It is also applicable to the problem for the stability of planar waves in the whole space or in the half space, and gives the optimal convergence rate toward the planar waves as time goes to infinity. This energy method makes use of several special interpolation inequalities.

Degenerate boundary layers for a system of viscous conservation laws

2016 ◽  
Vol 14 (01) ◽  
pp. 75-99
Author(s):  
Tohru Nakamura
Keyword(s):  
Boundary Layer ◽  
Asymptotic Stability ◽  
Conservation Laws ◽  
Type Inequality ◽  
A Priori Estimate ◽  
Hardy Type Inequality ◽  
Weighted Energy Method ◽  
Boundary Layer Solution ◽  
Viscous Conservation Laws ◽  
Layer Solution

This paper is concerned with existence and asymptotic stability of a boundary layer solution which is a smooth stationary wave for a system of viscous conservation laws in one-dimensional half space. With the aid of the center manifold theory, it is shown that the degenerate boundary layer solution exists under the situation that one characteristic is zero and the other characteristics are negative. Asymptotic stability of the degenerate boundary layer solution is also proved in an algebraically weighted Sobolev space provided that the weight exponent [Formula: see text] satisfies [Formula: see text]. The stability analysis is based on deriving the a priori estimate by using the weighted energy method combined with the Hardy type inequality with the best possible constant.

scholarly journals Time-weighted energy method for quasi-linear hyperbolic systems of viscoelasticity

2011 ◽  
Vol 87 (6) ◽  
pp. 99-102 ◽  
Author(s):  
Priyanjana M. N. Dharmawardane ◽  
Tohru Nakamura ◽  
Shuichi Kawashima
Keyword(s):  
Energy Method ◽  
Hyperbolic Systems ◽  
Weighted Energy Method ◽  
Weighted Energy

ASYMPTOTIC DECAY TOWARD THE PLANAR RAREFACTION WAVES OF SOLUTIONS FOR VISCOUS CONSERVATION LAWS IN SEVERAL SPACE DIMENSIONS

1996 ◽  
Vol 06 (03) ◽  
pp. 315-338 ◽  
Author(s):  
KAZUO ITO
Keyword(s):  
Conservation Laws ◽  
Decay Rate ◽  
Energy Method ◽  
Rarefaction Waves ◽  
Asymptotic Decay ◽  
One Dimensional ◽  
Viscous Conservation Laws ◽  
Asymptotic Decay Rate

This paper gives the asymptotic decay rate toward the planar rarefaction waves of the solutions for the scalar viscous conservation laws in two or more space dimensions. This is proved by a result on the decay rate of solutions for one-dimensional scalar viscous conservation laws and by using an L2-energy method with a weight of time.

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