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

Ádám Besenyei

Mathematica Bohemica (2010)

  • Volume: 135, Issue: 2, page 133-141
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Besenyei, Ádám. "On some nonlocal systems containing a parabolic PDE and a first order ODE." Mathematica Bohemica 135.2 (2010): 133-141. <http://eudml.org/doc/38117>.

@article{Besenyei2010,
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.},
author = {Besenyei, Ádám},
journal = {Mathematica Bohemica},
keywords = {Schauder fixed point theorem; system of parabolic and elliptic equations; monotone operator; reaction-diffusion; Schauder fixed point theorem; system of parabolic and elliptic equations; monotone operator; reaction-diffusion},
language = {eng},
number = {2},
pages = {133-141},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On some nonlocal systems containing a parabolic PDE and a first order ODE},
url = {http://eudml.org/doc/38117},
volume = {135},
year = {2010},
}

TY - JOUR
AU - Besenyei, Ádám
TI - On some nonlocal systems containing a parabolic PDE and a first order ODE
JO - Mathematica Bohemica
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 135
IS - 2
SP - 133
EP - 141
AB - 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.
LA - eng
KW - Schauder fixed point theorem; system of parabolic and elliptic equations; monotone operator; reaction-diffusion; Schauder fixed point theorem; system of parabolic and elliptic equations; monotone operator; reaction-diffusion
UR - http://eudml.org/doc/38117
ER -

References

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  7. Cinca, S., Diffusion und Transport in porösen Medien bei veränderlichen Porosität, Diplomawork, University of Heidelberg (2000). (2000) 
  8. Cohen, D. S., Jr., A. B. White, Whitelski, T. P., 10.1137/S0036139993269333, SIAM J. Appl. Math. 55 (1995), 348-368. (1995) MR1322764DOI10.1137/S0036139993269333
  9. Edwards, D. A., 10.1007/PL00001546, Z. Angew. Math. Phys. 52 (2001), 254-288. (2001) Zbl1160.35328MR1834529DOI10.1007/PL00001546
  10. Lions, J. L., Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Gauthier-Villars, Paris (1969). (1969) Zbl0189.40603MR0259693
  11. Logan, J. D., Petersen, M. R., Shores, T. S., 10.1016/S0096-3003(01)00052-2, Appl. Math. Comput. 127 (2002), 149-164. (2002) Zbl1016.86003MR1883122DOI10.1016/S0096-3003(01)00052-2
  12. Rivière, B., Shaw, S., 10.1137/05064480X, SIAM J. Numer. Anal. 44 (2006), 2650-2670. (2006) Zbl1135.65036MR2272610DOI10.1137/05064480X
  13. Simon, L., Application of monotone type operators to parabolic and functional parabolic PDE's, C. M. Dafermos, M. Pokorný Handbook of Differential Equations: Evolutionary Equations, vol 4., North-Holland, Amsterdam (2008), 267-321. (2008) MR2508168
  14. Simon, L., On some singular systems of parabolic functional differential equations, Submitted. 
  15. Zeidler, E., Nonlinear Functional Analysis and its Applications I, Springer (1986). (1986) Zbl0583.47050MR0816732

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