Scalar conservation laws on a half-line: A parabolic approach

Miriam Bank*, Matania Ben-Artzi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

The initial-boundary value problem for the (viscous) nonlinear scalar conservation law is considered, ut=∈u xx, xε ℝ+=(0,∞), 0≤t≤T, ∈≥0, u(x,o)=u0(x), u∈(0,t)=g(t).The flux f(ξ) ∈ C2() is assumed to be convex (but not strictly convex, i.e. f″(ξ)< 0). It is shown that a unique limit u = lim→0 uε exists. The classical duality method is used to prove uniqueness. To this end parabolic estimates for both the direct and dual solutions are obtained. In particular, no use is made of the Krukov entropy considerations.

Original languageEnglish
Pages (from-to)165-189
Number of pages25
JournalJournal of Hyperbolic Differential Equations
Volume7
Issue number1
DOIs
StatePublished - Mar 2010

Keywords

  • Duality method
  • Initial-boundary value problem
  • Scalar conservation law
  • Uniqueness
  • Zero viscosity limit

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