Asymptotic stability of rarefaction wave of the Cauchy problem for viscous conservation laws

2005 ◽  
Vol 61 (1-2) ◽  
pp. 115-133 ◽  
Author(s):  
Yanping Dou
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Stability ◽  
Conservation Laws ◽  
Rarefaction Wave ◽  
Viscous Conservation Laws ◽  
The Cauchy Problem

ASYMPTOTIC STABILITY OF NON-PLANAR RIEMANN SOLUTIONS FOR MULTI-D SYSTEMS OF CONSERVATION LAWS WITH SYMMETRIC NONLINEARITIES

2004 ◽  
Vol 01 (03) ◽  
pp. 567-579 ◽  
Author(s):  
HERMANO FRID
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Asymptotic Stability ◽  
Conservation Laws ◽  
Entropy Solution ◽  
Smooth Functions ◽  
Riemann Solutions ◽  
The Cauchy Problem ◽  
Systems Of Conservation Laws ◽  
Self Similar

We study the asymptotic behavior of entropy solutions of the Cauchy problem for multi-dimensional systems of conservation laws of the form [Formula: see text], where the gα are real smooth functions defined in [0,+∞), and when the initial data are perturbations of two-state nonplanar Riemann data. Specifically, if R0(x) is such Riemann data and ψ∈L∞(ℝd)n satisfies ψ(Tx)→0 in [Formula: see text], as T→∞, then an entropy solution, u(x,t), of the Cauchy problem with u(x,0)=R0(x)+ψ(x) satisfies u(ξt,t)→R(ξ) in [Formula: see text], as t→∞, where R(x/t) turns out to be the unique self-similar entropy solution of the corresponding Riemann problem.

scholarly journals Nonlinear conservation laws for the Schrödinger boundary value problems of second order

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ming Ren ◽  
Shiwei Yun ◽  
Zhenping Li
Keyword(s):  
Cauchy Problem ◽  
Conservation Laws ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Maximum Modulus ◽  
Second Order ◽  
Nonlinear Conservation Laws ◽  
The Cauchy Problem ◽  
Modulus Method ◽  
Semilinear Schrödinger Equation

AbstractIn this paper, we apply a reliable combination of maximum modulus method with respect to the Schrödinger operator and Phragmén–Lindelöf method to investigate nonlinear conservation laws for the Schrödinger boundary value problems of second order. As an application, we prove the global existence to the solution for the Cauchy problem of the semilinear Schrödinger equation. The results reveal that this method is effective and simple.

scholarly journals Nonclassical Shocks and the Cauchy Problem for Nonconvex Conservation Laws

1999 ◽  
Vol 151 (2) ◽  
pp. 345-372 ◽  
Author(s):  
D. Amadori ◽  
P. Baiti ◽  
P.G. LeFloch ◽  
B. Piccoli
Keyword(s):  
Cauchy Problem ◽  
Conservation Laws ◽  
The Cauchy Problem
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