LP decay for general hyperbolic-parabolic systems of balance laws

Academic Article

Abstract

  • We study time asymptotic decay of solutions for a general system of hyperbolic-parabolic balance laws in multi space dimensions. The system has physical viscosity matrices and a lower order term for relaxation, damping or chemical reaction. The viscosity matrices and the Jacobian matrix of the lower order term are rank deficient. For Cauchy problem around a constant equilibrium state, existence of solution global in time has been established recently under a set of reasonable assumptions. In this paper we obtain optimal LP decay rates for p ≥ 2. Our result is general and applies to physical models such as gas ows with translational and vibrational non-equilibrium. Our result also recovers or improves the existing results in literature on the special cases of hyper.
  • Authors

    Digital Object Identifier (doi)

    Author List

  • Zeng Y
  • Start Page

  • 363
  • End Page

  • 396
  • Volume

  • 38
  • Issue

  • 1