Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 79, Issue 5, Pages 1990-2010Publisher
SIAM PUBLICATIONS
DOI: 10.1137/19M1250261
Keywords
virus infection; chemotaxis; pattern formation; global existence; asymptotics
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Funding
- National Natural Science Foundation of China [11861131003]
- Deutsche Forschungsgemeinschaft in the framework of the project Emergence of Structures and Advantages in Cross-Diffusion Systems [411007140, GZ: WI 3707/5-1]
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This work focuses on an extension to the May-Nowak model for virus dynamics, additionally accounting for diffusion in all components and chemotactically directed motion of healthy cells in response to density gradients in the population of infected cells. The first part of the paper presents a number of simulations with the aim of investigating how far the model can depict interesting patterns. A rigorous analysis of the initial-boundary value problem is presented in a second part, where a statement on global classical solvability for arbitrarily large initial data is derived under an appropriate smallness assumption on the chemotactic coefficient. Two additional results on asymptotic stabilisation indicate that the so-called basic reproduction number retains its crucial influence on the large time behavior of solutions, as is well-known from results on the May-Nowak system.
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