Geodesic
On some nonlocal systems containing a parabolic PDE and a first order ODE
Mathematica Bohemica, Tome 135 (2010) no. 2, pp. 133-141

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MR Zbl
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.
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.
DOI : 10.21136/MB.2010.140690
Classification : 35J60, 35K60
Keywords: Schauder fixed point theorem; system of parabolic and elliptic equations; monotone operator; reaction-diffusion 
Besenyei, Ádám. On some nonlocal systems containing a parabolic PDE and a first order ODE. Mathematica Bohemica, Tome 135 (2010) no. 2, pp. 133-141. doi: 10.21136/MB.2010.140690
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