| Title:
|
On some nonlocal systems containing a parabolic PDE and a first order ODE (English) |
| Author:
|
Besenyei, Ádám |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
135 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
133-141 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Schauder fixed point theorem |
| Keyword:
|
system of parabolic and elliptic equations |
| Keyword:
|
monotone operator |
| Keyword:
|
reaction-diffusion |
| MSC:
|
35J60 |
| MSC:
|
35K60 |
| idZBL:
|
Zbl 1224.35221 |
| idMR:
|
MR2723080 |
| DOI:
|
10.21136/MB.2010.140690 |
| . |
| Date available:
|
2010-07-20T18:30:31Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140690 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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[3] Hu, B., Zhang, J.: Global existence for a class of non-Fickian polymer-penetrant systems.J. Partial Differ. Equations 9 (1996), 193-208. MR 1413446 |
| Reference:
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[4] Besenyei, Á.: On a nonlinear system consisting of three different types of differential equations.Acta Math. Hungar. (2009). MR 2629675 |
| Reference:
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| Reference:
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| Reference:
|
[7] Cinca, S.: Diffusion und Transport in porösen Medien bei veränderlichen Porosität.Diplomawork, University of Heidelberg (2000). |
| Reference:
|
[8] Cohen, D. S., Jr., A. B. White, Whitelski, T. P.: Shock formation on a multidimensional viscoelastic diffusive systems.SIAM J. Appl. Math. 55 (1995), 348-368. MR 1322764, 10.1137/S0036139993269333 |
| Reference:
|
[9] Edwards, D. A.: A spatially nonlocal model for polymer-penetrant-diffusion.Z. Angew. Math. Phys. 52 (2001), 254-288. Zbl 1160.35328, MR 1834529, 10.1007/PL00001546 |
| Reference:
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[10] Lions, J. L.: Quelques méthodes de résolution des problèmes aux limites non linéaires.Dunod, Gauthier-Villars, Paris (1969). Zbl 0189.40603, MR 0259693 |
| Reference:
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[11] Logan, J. D., Petersen, M. R., Shores, T. S.: Numerical study of reaction-mineralogy-porosity changes in porous media.Appl. Math. Comput. 127 (2002), 149-164. Zbl 1016.86003, MR 1883122, 10.1016/S0096-3003(01)00052-2 |
| Reference:
|
[12] Rivière, B., Shaw, S.: Discontinuous Galerkin finite element approximation of nonlinear non-Fickian diffusion in viscoelastic polymers.SIAM J. Numer. Anal. 44 (2006), 2650-2670. Zbl 1135.65036, MR 2272610, 10.1137/05064480X |
| Reference:
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[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. MR 2508168 |
| Reference:
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| Reference:
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| . |
