Mathematical analysis of an in-host model of viral dynamics with spatial heterogeneity
S Pankavich, C Parkinson - arXiv preprint arXiv:1508.07617, 2015 - arxiv.org
We consider a spatially-heterogeneous generalization of a well-established model for the
dynamics of the Human Immunodeficiency Virus-type 1 (HIV) within a susceptible host. The …
dynamics of the Human Immunodeficiency Virus-type 1 (HIV) within a susceptible host. The …
[HTML][HTML] Spatially homogeneous solutions of the Vlasov–Nordström–Fokker–Planck system
Abstract The Vlasov–Nordström–Fokker–Planck system describes the evolution of self-
gravitating matter experiencing collisions with a fixed background of particles in the …
gravitating matter experiencing collisions with a fixed background of particles in the …
A short proof of increased parabolic regularity
S Pankavich, N Michalowski - arXiv preprint arXiv:1502.01773, 2015 - arxiv.org
We present a new, short proof of the increased regularity obtained by solutions to uniformly
parabolic partial differential equations. Though this setting is fairly introductory, our new …
parabolic partial differential equations. Though this setting is fairly introductory, our new …
Global Classical Solutions of the one and one-half dimensional Vlasov-Maxwell Fokker-Planck System
S Pankavich, J Schaeffer - arXiv preprint arXiv:1502.01777, 2015 - arxiv.org
We study the" one and one-half" dimensional Vlasov-Maxwell-Fokker-Planck system and
obtain the first results concerning well-posedness of solutions. Specifically, we prove the …
obtain the first results concerning well-posedness of solutions. Specifically, we prove the …
The Vlasov-Maxwell-Fokker-Planck system with relativistic transport in the whole space
Y Dongcheng - Acta Mathematica Scientia, 2017 - Elsevier
In this paper, we consider the Vlasov-Maxwell-Fokker-Planck system with relativistic
transport in the whole space. The global solutions to this system near the relativistic …
transport in the whole space. The global solutions to this system near the relativistic …
The Vlasov–Maxwell–Fokker–Planck system near Maxwellians in ℝ3
X Wang - Applicable Analysis, 2021 - Taylor & Francis
ABSTRACT Motivated by Duan and Strain [Optimal large-time behavior of the Vlasov–
Maxwell–Boltzmann system in the whole space. Comm Pure Appl Math. 2011; 64: 1497 …
Maxwell–Boltzmann system in the whole space. Comm Pure Appl Math. 2011; 64: 1497 …
A relativistic diffusion model in kinetic theory
JA Alcántara Félix - 2016 - digibug.ugr.es
The main objective of this dissertation is the analysis of solutions to a class of linear and non-
linear parabolic partial differential equations (PDEs) in phase space for dimensions greater …
linear parabolic partial differential equations (PDEs) in phase space for dimensions greater …
Global mild solutions to the Vlasov-Maxwell-Fokker-Planck system
Y Fan, Y Lei - arXiv preprint arXiv:2112.00244, 2021 - arxiv.org
Motivated by Duan et al.[Global Mild Solutions of the Landau and Non-Cutoff Boltzmann
Equations, Comm. Pure Appl. Math., 74 (5), 932-1020.], the global existence of mild …
Equations, Comm. Pure Appl. Math., 74 (5), 932-1020.], the global existence of mild …
The Vlasov–Maxwell–Fokker–Planck system in two space dimensions
J Schaeffer - Mathematical Methods in the Applied Sciences, 2016 - Wiley Online Library
We consider the Cauchy problem for the Vlasov–Maxwell–Fokker–Planck system in the
plane. It is shown that for smooth initial data, as long as the electromagnetic fields remain …
plane. It is shown that for smooth initial data, as long as the electromagnetic fields remain …
On the spatially homogeneous and isotropic Einstein-Vlasov-Fokker-Planck system with cosmological scalar field
S Calogero, S Pankavich - arXiv preprint arXiv:1606.05101, 2016 - arxiv.org
The Einstein-Vlasov-Fokker-Planck system describes the kinetic diffusion dynamics of self-
gravitating particles within the Einstein theory of general relativity. We study the Cauchy …
gravitating particles within the Einstein theory of general relativity. We study the Cauchy …