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Keywords:
parabolic functional equation; singular system; monotone type operator
Summary:
We will prove existence of weak solutions of a system, containing non-local terms $u$, $w$. \endabstract
References:
[1] Adams, R. A.: Sobolev Spaces. Academic Press, New York (1975). MR 0450957 | Zbl 0314.46030
[2] Amann, H.: Highly degenerate quasilinear parabolic systems. Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 18 (1991), 136-166. MR 1118224 | Zbl 0738.35029
[3] Berkovits, J., Mustonen, V.: Topological degreee for perturbations of linear maximal monotone mappings and applications to a class of parabolic problems. Rend. Mat. Appl. VII. 12 (1992), 597-621. MR 1205967
[4] Cinca, S.: Diffusion und Transport in porösen Medien bei veränderlichen Porosität. Diplomawork, Univ. Heidelberg (2000).
[5] Hu, Bei, Zhang, Jianhua: Global existence for a class of non-Fickian polymer-penetrant systems. J. Part. Diff. Eq. 9 (1996), 193-208. MR 1413446
[6] 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. DOI 10.1016/S0096-3003(01)00052-2 | MR 1883122 | Zbl 1016.86003
[7] Merkin, J. H., Needham, D. J., Sleeman, B. D.: A mathematical model for the spread of morphogens with density dependent chemosensitivity. Nonlinearity 18 (2005), 2745-2773. DOI 10.1088/0951-7715/18/6/018 | MR 2176957 | Zbl 1078.92010
[8] 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. DOI 10.1137/05064480X | MR 2272610 | Zbl 1135.65036
[9] Simon, L., Jäger, W.: On non-uniformly parabolic functional differential equations. Stud. Sci. Math. Hung. 45 (2008), 285-300. MR 2417974 | Zbl 1174.35054
[10] Simon, L.: Application of monotone type operators to parabolic and functional parabolic PDE's. Handbook of Differential Equations. Evolutionary Equations, Vol. 4, Elsevier (2008), 267-321. DOI 10.1016/S1874-5717(08)00006-6 | MR 2508168
[11] Zeidler, E.: Nonlinear Functional Analysis and Its Applications II A and II B. Springer (1990). MR 1033497
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