scholarly journals Stability of the 1D IBVP for a non autonomous scalar conservation law

2018 ◽  
Vol 149 (03) ◽  
pp. 561-592 ◽  
Author(s):  
Rinaldo M. Colombo ◽  
Elena Rossi
Keyword(s):  
Conservation Laws ◽  
Boundary Value Problems ◽  
Conservation Law ◽  
Space Dimension ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Scalar Conservation Law ◽  
Scalar Conservation ◽  
The Stability ◽  
Initial Boundary Value

We prove the stability with respect to the flux of solutions to initial – boundary value problems for scalar non autonomous conservation laws in one space dimension. Key estimates are obtained through a careful construction of the solutions.

scholarly journals Accurate numerical schemes for approximating initial-boundary value problems for systems of conservation laws

2015 ◽  
Vol 12 (01) ◽  
pp. 61-86 ◽  
Author(s):  
Siddhartha Mishra ◽  
Laura V. Spinolo
Keyword(s):  
Conservation Laws ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Numerical Schemes ◽  
Systems Of Conservation Laws ◽  
Initial Boundary Value ◽  
Limit Solutions ◽  
Viscous Mechanism

Solutions of initial-boundary value problems for systems of conservation laws depend on the underlying viscous mechanism, namely different viscosity operators lead to different limit solutions. Standard numerical schemes for approximating conservation laws do not take into account this fact and converge to solutions that are not necessarily physically relevant. We design numerical schemes that incorporate explicit information about the underlying viscosity mechanism and approximate the physical-viscosity solution. Numerical experiments illustrating the robust performance of these schemes are presented.

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