viscous conservation laws
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L2-type contraction of viscous shocks for scalar conservation laws

2021 ◽  
Vol 18 (02) ◽  
pp. 271-292
Author(s):  
Logan F. Stokols
Keyword(s):  
Conservation Laws ◽  
Entropy Method ◽  
Uniformly Convex ◽  
Scalar Conservation Laws ◽  
Nonlinear Dissipation ◽  
Spatially Inhomogeneous ◽  
Viscous Conservation Laws ◽  
Scalar Conservation ◽  
Relative Entropy Method ◽  
Type Contraction

We study small shocks of 1D scalar viscous conservation laws with uniformly convex flux and nonlinear dissipation. We show that such shocks are [Formula: see text] stable independently of the strength of the dissipation, even with large perturbations. The proof uses the relative entropy method with a spatially-inhomogeneous pseudo-norm.

scholarly journals Viscous conservation laws in 1D with measure initial data

2020 ◽  
Vol 79 (1) ◽  
pp. 103-124
Author(s):  
Miriam Bank ◽  
Matania Ben-Artzi ◽  
Maria E. Schonbek
Keyword(s):  
Initial Data ◽  
Conservation Laws ◽  
Viscous Conservation Laws

scholarly journals Stability properties and dynamics of solutions to viscous conservation laws with mean curvature operator

2019 ◽  
Vol 20 (2) ◽  
pp. 517-551 ◽  
Author(s):  
Raffaele Folino ◽  
Maurizio Garrione ◽  
Marta Strani
Keyword(s):  
Conservation Laws ◽  
Mean Curvature ◽  
Curvature Operator ◽  
Stability Properties ◽  
Viscous Conservation Laws ◽  
Mean Curvature Operator

scholarly journals L2-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws

2019 ◽  
Vol 267 (5) ◽  
pp. 2737-2791 ◽  
Author(s):  
Moon-Jin Kang ◽  
Alexis F. Vasseur ◽  
Yi Wang
Keyword(s):  
Shock Waves ◽  
Conservation Laws ◽  
Viscous Conservation Laws ◽  
Planar Shock
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