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Well posedness of an angiogenesis related integrodifferential diffusion model

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Carpio, Ana and Duro, Gema (2016) Well posedness of an angiogenesis related integrodifferential diffusion model. Applied Mathematical Modelling, 40 (9-10). pp. 5560-5575. ISSN 0307904X

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Official URL: https://doi.org/10.1016/j.apm.2016.01.025




Abstract

We prove existence and uniqueness of nonnegative solutions for a nonlocal in time integrodifferential diffusion system related to angiogenesis descriptions. Fundamental solutions of appropriately chosen parabolic operators with bounded coefficients allow us to generate sequences of approximate solutions. Comparison principles and integral equations provide uniform bounds ensuring some convergence properties for iterative schemes and providing stability bounds.
Uniqueness follows from chained integral inequalities.


Item Type:Article
Uncontrolled Keywords:Integrodifferential, Diffusion, Nonlocal, Fundamental solutions
Subjects:Sciences > Mathematics > Differential equations
Sciences > Mathematics > Operations research
Medical sciences > Medicine > Cardiovascular system
ID Code:55542
Deposited On:31 May 2019 17:29
Last Modified:03 Jun 2019 07:23

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