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Title: Lp time asymptotic decay for general hyperbolic–parabolic balance laws with applications
We study the time asymptotic decay of solutions for a general system of hyperbolic–parabolic balance laws in one space dimension. The system has a physical viscosity matrix and a lower-order term for relaxation, damping or chemical reaction. The viscosity matrix 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 [Formula: see text] decay rates for [Formula: see text]. Our result is general and applies to models such as Keller–Segel equations with logarithmic chemotactic sensitivity and logistic growth, and gas flows with translational and vibrational non-equilibrium. Our result also recovers or improves the existing results in literature on the special cases of hyperbolic–parabolic conservation laws and hyperbolic balance laws, respectively.  more » « less
Award ID(s):
1908195
PAR ID:
10155910
Author(s) / Creator(s):
Date Published:
Journal Name:
Journal of Hyperbolic Differential Equations
Volume:
16
Issue:
04
ISSN:
0219-8916
Page Range / eLocation ID:
663 to 700
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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