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Abstract. 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(More)
This work is concerned with time-asymptotic stability of boundarylayers for a typical hyperbolic relaxation system. Under a nonclassical requirement characterizing a class of boundary conditions for the typical system, we prove the global (in time) existence and asymptotic decay of solutions with initial data close to the steady solutions or relaxation(More)
We analyze a mathematical model for the relaxation of translational and internal temperatures in a nonequilibrium gas. The system of partial differential equations—derived from the kinetic theory of gases—is recast in its natural entropic symmetric form as well as in a convenient hyperbolic-parabolic symmetric form. We investigate the Chapman-Enskog(More)
In this work, we derive a simple mathematical model from mass-action equations for amyloid fiber formation that takes into account the primary nucleation, elongation, and length-dependent fragmentation. The derivation is based on the principle of minimum free energy under certain constraints and is mathematically related to the partial equilibrium(More)
We prove that no H theorem exists for the athermal lattice Boltzmann equation with polynomial equilibria satisfying the conservation laws exactly and explicitly. The proof is demonstrated by using the seven-velocity model in a triangular lattice in two dimensions, and can be readily extended to other lattice Boltzmann models in two and three dimensions.(More)