MATHEMATICA BOHEMICA, Vol. 135, No. 2, pp. 133-141, 2010

On some nonlocal systems containing
a parabolic PDE and a first order ODE

Adam Besenyei

Adam Besenyei, Eotvos Lorand University, H-1117 Budapest, Pazmany P. s. 1/C, Hungary, e-mail: badam@cs.elte.hu

Abstract: Two models of reaction-diffusion are presented: a non-Fickian diffusion model described by a system of a parabolic PDE and a first order ODE, further, porosity-mineralogy changes in porous medium which is modelled by a system consisting of an ODE, a parabolic and an elliptic equation. Existence of weak solutions is shown by the Schauder fixed point theorem combined with the theory of monotone type operators.

Keywords: Schauder fixed point theorem, system of parabolic and elliptic equations, monotone operator, reaction-diffusion

Classification (MSC 2010): 35K60, 35J60

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