Convergence of Approximate Solutions of the Cauchy Problem for a 2×2 Nonstrictly Hyperbolic System of Conservation Laws

1993 ◽  
pp. 487-494 ◽  
Author(s):  
Bruno Rubino
Keyword(s):  
Cauchy Problem ◽  
Conservation Laws ◽  
Hyperbolic System ◽  
Approximate Solutions ◽  
System Of Conservation Laws ◽  
The Cauchy Problem ◽  
Convergence Of Approximate Solutions

Global BV solutions and relaxation limit for a system of conservation laws

2001 ◽  
Vol 131 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Debora Amadori ◽  
Graziano Guerra
Keyword(s):  
Cauchy Problem ◽  
Nonlinear System ◽  
Conservation Laws ◽  
Bounded Variation ◽  
Equilibrium Curve ◽  
Equilibrium Equations ◽  
System Of Conservation Laws ◽  
The Cauchy Problem ◽  
Image Position

We consider the Cauchy problem for the (strictly hyperbolic, genuinely nonlinear) system of conservation laws with relaxation Assume there exists an equilibrium curve A(u), such that r(u,A(u)) = 0. Under some assumptions on σ and r, we prove the existence of global (in time) solutions of bounded variation, uε, υε, for ε > 0 fixed.As ε → 0, we prove the convergence of a subsequence of uε, υε to some u, υ that satisfy the equilibrium equations

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.

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