Develops and analyzes hypocoercivity-preserving C0-IP finite-element methods in space with hp-DG time stepping for kinetic Fokker-Planck equations on R^d x R^d, proving exponential decay via weighted Poincare inequalities and new trace estimates.
Short and long time behavior of the
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Constructs weak solutions, proves anisotropic Besov regularity, and establishes uniqueness in the mass-preserving renormalized class for kinetic FP equations with nonlinear diffusion under mass-critical growth on Ψ.
citing papers explorer
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Hypocoercivity-preserving space-time Galerkin methods for kinetic Fokker-Planck equations
Develops and analyzes hypocoercivity-preserving C0-IP finite-element methods in space with hp-DG time stepping for kinetic Fokker-Planck equations on R^d x R^d, proving exponential decay via weighted Poincare inequalities and new trace estimates.
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Kinetic Fokker-Planck Equations with Nonlinear Diffusion
Constructs weak solutions, proves anisotropic Besov regularity, and establishes uniqueness in the mass-preserving renormalized class for kinetic FP equations with nonlinear diffusion under mass-critical growth on Ψ.