Kinetic and Related Models
October 2020 , Volume 13 , Issue 5
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A particular 2x2 hyperbolic system commonly used in the context of gas-solid chromatography is reformulated as a single kinetic equation using an additional kinetic variable. A kinetic numerical scheme is built from this new formulation and its behavior is tested on solving the Riemann problem in different configurations leading to single or composite waves.
In this paper, we present quantitative local sensitivity estimates for the kinetic chemotaxis Cucker-Smale(CCS) equation with random inputs. In the absence of random inputs, the kinetic CCS model exhibits velocity alignment under suitable structural assumptions on the turning kernel and reaction term despite of the random effect due to a turning operator. We provide a global existence of a regular solution with slow velocity alignment for the random kinetic CCS model within the proposed framework. Moreover, we investigate the propagation of regularity and stability of infinitesimal variations in random space.
If the Vlasov-Poisson or Einstein-Vlasov system is linearized about an isotropic steady state, a linear operator arises the properties of which are relevant in the linear as well as nonlinear stability analysis of the given steady state. We prove that when defined on a suitable Hilbert space and equipped with the proper domain of definition this transport operator
We consider the Cauchy problem of the nonlinear Landau equation of Maxwellian molecules, under the perturbation frame work to global equilibrium. We show that if
We study the emergent behavior of discrete-time approximation of the finite-dimensional Kuramoto model. Compared to Zhang and Zhu's recent work in [
The aim of the article is to study the stability of a non-local kinetic model proposed in [
In this work we consider the Cauchy problem for the spatially inhomogeneous non-cutoff Boltzmann equation. For any given solution belonging to weighted Sobolev space, we will show it enjoys at positive time the Gelfand-Shilov smoothing effect for the velocity variable and Gevrey regularizing properties for the spatial variable. This improves the result of Lerner-Morimoto-Pravda-Starov-Xu [J. Funct. Anal. 269 (2015) 459-535] on one-dimensional Boltzmann equation to the physical three-dimensional case. Our proof relies on the elementary
We investigate the global existence of weak solutions to a free boundary problem governing the evolution of finitely extensible bead-spring chains in dilute polymers. The free boundary in the present context is defined with regard to a density threshold of
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