Communications in Mathematical Physics

, Volume 187, Issue 2, pp 327–340

Existence of Solutions to Hyperbolic Conservation Laws with a Source

  • Christian Klingenberg
  • Yun-guang Lu

DOI: 10.1007/s002200050138

Cite this article as:
Klingenberg, C. & Lu, Y. Comm Math Phys (1997) 187: 327. doi:10.1007/s002200050138


Existence of solutions to three different systems of Eqs. (1.1), (1.2) and (1.3) coming from physically relevant models is shown, each needing a different proof which are given in Sects. 2, 3 and 4. The unifying theme is the presence of source terms and the general method of proof is vanishing viscosity together with compensated compactness. For system (1.2) entropy-entropy flux pairs of Lax type are constructed and estimates from singular perturbation theory of ODEs are used. For (1.1) and (1.3) weak entropy-entropy flux pairs are constructed following the compensated compactness framework set up by Diperna [4].

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Christian Klingenberg
    • 1
  • Yun-guang Lu
    • 2
  1. 1.Applied Mathematics, Würzburg University, Am Hubland, Würzburg 97074, GermanyDE
  2. 2.Young Scientist Laboratory of Mathematical Physics, Wuhan Institute of Mathematical Sciences, Academia Sinica, Wuhan, ChinaCN

Personalised recommendations