1. REACTION-DIFFUSION-ADVECTION SYSTEMS WITH DISCONTINUOUS DIFFUSION AND MASS CONTROL.
- Author
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FITZGIBBON, WILLIAM E., MORGAN, JEFFREY J., TANG, BAO Q., and HONG-MING YIN
- Subjects
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DIFFUSION control , *ADVECTION-diffusion equations , *DIFFERENTIAL operators , *HUMAN behavior models , *INFECTIOUS disease transmission , *COMMUNICABLE diseases - Abstract
In this paper, we study unique, globally defined uniformly bounded weak solutions for a class of semilinear reaction-diffusion-advection systems. The coefficients of the differential operators and the initial data are only required to be measurable and uniformly bounded. The nonlinearities are quasi-positive and satisfy a commonly called mass control or dissipation of mass property. Moreover, we assume the intermediate sum condition of a certain order. The key feature of this work is the surprising discovery that quasi-positive systems that satisfy an intermediate sum condition automatically give rise to a new class of Lp-energy type functionals that allow us to obtain requisite uniform a priori bounds. Our methods are sufficiently robust to extend to different boundary conditions, or to certain quasi-linear systems. We also show that in the case of mass dissipation, the solution is bounded in sup-norm uniformly in time. We illustrate the applicability of results by showing global existence and large time behavior of models arising from a spatio-temporal spread of infectious disease. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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