Convergence in the form of a solution to the Cauchy problem for a quasilinear parabolic equation with a monotone initial condition to a system of waves

Article

DOI: 10.1134/S0965542508080095

Cite this article as:
Gasnikov, A.V. Comput. Math. and Math. Phys. (2008) 48: 1376. doi:10.1134/S0965542508080095
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Abstract

The time asymptotic behavior of a solution to the initial Cauchy problem for a quasilinear parabolic equation is investigated. Such equations arise, for example, in traffic flow modeling. The main result of this paper is the proof of the previously formulated conjecture that, if a monotone initial function has limits at plus and minus infinity, then the solution to the Cauchy problem converges in form to a system of traveling and rarefaction waves; furthermore, the phase shifts of the traveling waves may depend on time. It is pointed out that the monotonicity condition can be replaced with the boundedness condition.

Keywords

conservation law with nonlinear divergent viscosity convergence in form traveling wave rarefaction wave system of waves Cauchy problem for a quasilinear parabolic equation 

Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  1. 1.Moscow Institute of Physics and Technology (MFTI, State University)Dolgoprudnyi, Moscow oblastRussia

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