A necessary and sufficient condition for global existence for a quasilinear reaction-diffusion system.
Lair, Alan V. (2005)
International Journal of Mathematics and Mathematical Sciences
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Lair, Alan V. (2005)
International Journal of Mathematics and Mathematical Sciences
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Zejia, Wang, Jingxue, Yin (2003)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Ádám Besenyei (2010)
Mathematica Bohemica
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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.