Publicación: PATTERN FORMATION FOR A REACTION DIFFUSION SYSTEM WITH CONSTANT AND CROSS DIFFUSION
Fecha
2014
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LECTURE NOTES IN COMPUTATIONAL SCIENCE AND ENGINEERING, NUMERICAL MATHEMATICS AND ADVANCED APPLICATIONS
Resumen
IN THIS WORK, WE STUDY A FINITE VOLUME SCHEME FOR A REACTION DIFFUSION SYSTEM WITH CONSTANT AND CROSS DIFFUSION MODELING THE SPREAD OF AN EPIDEMIC DISEASE WITHIN A HOST POPULATION STRUCTURED WITH THREE SUBCLASSES OF INDIVIDUALS (SIR-MODEL). THE MOBILITY IN EACH CLASS IS ASSUMED TO BE INFLUENCED BY THE GRADIENT OF OTHER CLASSES. WE ESTABLISH THE EXISTENCE OF A SOLUTION TO THE FINITE VOLUME SCHEME AND SHOW CONVERGENCE TO A WEAK SOLUTION. THE CONVERGENCE PROOF IS BASED ON DERIVING A SERIES OF A PRIORI ESTIMATES AND USING A GENERAL L P COMPACTNESS CRITERION.
