Validity of nonlinear geometric optics for entropy solutions of multidimensional scalar conservation laws

Journal article

Nonlinear geometric optics with various frequencies for entropy solutions only in L∞ of multidimensional scalar conservation laws is analyzed. A new approach to validate nonlinear geometric optics is developed via entropy dissipation through scaling, compactness, homogenization, and L1-stability. New multidimensional features are recognized, especially including nonlinear propagations of oscillations with high frequencies. The validity of nonlinear geometric optics for entropy solutions in L∞ of multidimensional scalar conservation laws is justified. © 2005 Elsevier Inc. All rights reserved.

Authors: Chen, G; Junca, S; Rascle, M

• Journal: Journal of Differential Equations
• Volume: 222
• Issue: 2
• Pages: 439-475
• Publication date: 2006-03-15
• DOI: 10.1016/j.jde.2005.04.014
• ISSN: 0022-0396
• Language: English
• Keywords: Multidimensional conservation laws; Compactness; Multiscale; Validity; Perturbation; Oscillation; Profile; Nonlinear geometric optics; Homogenization; New approach; Scaling; Entropy dissipation; BV; Stability; Entropy solutions in L∞