Stability for implicit–explicit schemes for non-equilibrium kinetic systems in weighted spaces with symmetrization

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Abstract

We consider kinetic systems, and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include advective and diffusive transport coupled to the accumulation of immobile components governed by non-equilibrium relationships. We also discuss extensions to nonlinear relationships and multiple species.

Keywords

Stability for systems
Kinetic models
Non-equilibrium
Adsorption
Implicit schemes
Explicit schemes

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Research partially supported by NSF DMS-1115827 “Hybrid modeling in porous media”, and NSF DMS-1522734 “Phase transitions in porous media across multiple scales”.