This work develops a singular perturbation theory for initial-value problems of nonlinear rst-order hyperbolic systems with stii source terms in several space variables. It is observed that under reasonable assumptions, many equations of classical physics of that type admit a structural stability condition. This condition is equivalent to the well-known… (More)
A stii system of conservation laws is analyzed with a diierence method. The existence of entropy-satisfying BV-solutions to the initial value problems is estabilished. Furthermore, we show that the solutions converge to the solutions of the corresponding equilibrium system as the relaxation time tends to zero.
This paper presents an observation that under reasonable conditions, many partial differential equations from mathematical physics possess three structural properties. One of them can be understand as a variant of the celebrated Onsager reciprocal relation in Modern Thermodynamics. It displays a direct relation of irreversible processes to the entropy… (More)
This note presents a simple approach toward interaction estimates of elementary waves for hyperbolic conservation laws. The new approach uses neither the Taylor expansion nor induction. The same technique is used to simplify the diierent interaction estimates in studying nonhomogeneous systems and initial-boundary value problems with Glimm's scheme. 1.… (More)
It is well known that the formation of amyloid fiber may cause invertible damage to cells, although the underlying mechanism has not been fully understood. In this article, a microscopic model considering the detailed processes of amyloid formation and cell damage is constructed based on four simple assumptions, one of which is that cell damage is raised by… (More)
In this paper, we provide a set of sufficient conditions under which a lattice Boltzmann model does not admit an H theorem. By verifying the conditions, we prove that a number of existing lattice Boltzmann models does not admit an H theorem. These models include D2Q6, D2Q9 and D3Q15 athermal models , and D2Q16 and D3Q40 thermal (energy-conserving) models.… (More)