Existence of renormalized solutions for nonlinear parabolic systems describing the spread of epidemics
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1437-1448.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we study the existence of nonnegative renormalized solutions for a class of nonlinear parabolic systems. Such systems describes the spread of epidemic disease from affected to unaffected individuals by contact infection.
Keywords: nonlinear parabolic systems, renormalized solutions.
@article{SEMR_2019_16_a101,
     author = {E. R. Andriyanova},
     title = {Existence of renormalized solutions for nonlinear parabolic systems describing the spread of epidemics},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1437--1448},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a101/}
}
TY  - JOUR
AU  - E. R. Andriyanova
TI  - Existence of renormalized solutions for nonlinear parabolic systems describing the spread of epidemics
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2019
SP  - 1437
EP  - 1448
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2019_16_a101/
LA  - ru
ID  - SEMR_2019_16_a101
ER  - 
%0 Journal Article
%A E. R. Andriyanova
%T Existence of renormalized solutions for nonlinear parabolic systems describing the spread of epidemics
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2019
%P 1437-1448
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2019_16_a101/
%G ru
%F SEMR_2019_16_a101
E. R. Andriyanova. Existence of renormalized solutions for nonlinear parabolic systems describing the spread of epidemics. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1437-1448. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a101/

[1] M. Bendahmane, M. Langlais, “A reaction-diffusion system with cross-diffusion modeling the spread of an epidemic disease”, Journal of Evolution Equations, 10:4 (2010), 883–904 | MR | Zbl

[2] M. Bendahmane, M. Langlais, M. Saad, “On some anisotropic reaction-diffusion systems with $L^1$-data modeling the propagation of an epidemic disease”, Nonlinear Analysis, 54:4 (2003), 617–636 | MR | Zbl

[3] M. Mimura, K. Kawasaki, “Spatial Segregation in Competitive Interactlon-Diffusion Equations”, J. Math. Biology, 9 (1980), 49–64 | MR | Zbl

[4] L. Shangerganesh, K. Balachandran, “Renormalized and entropy solutions of nonlinear parabolic system”, Electronic Journal of Differential Equations, 2013 (2013), Paper 268 | MR | Zbl

[5] F. Kh. Mukminov, “Suschestvovanie renormalizovannogo resheniya anizotropnoi parabolicheskoi zadachi dlya uravneniya s diffuznoi meroi”, Tr. Mat. Inst. Steklova, 306, 2019 (to appear)

[6] F. Kh. Mukminov, “Uniqueness of the renormalized solution of an elliptic-parabolic problem in anisotropic Sobolev-Orlicz spaces”, Sb. Math., 208:8 (2017), 1187–1206 | MR | Zbl

[7] J. Carrillo, P. Wittbold, “Uniqueness of renormalized solutions of degenerate elliptic-parabolic problems”, J. Differential Equations, 156:1 (1999), 93–121 | MR | Zbl

[8] H. W. Alt, S. Luckhaus, “Quasilinear elliptic-parabolic differential equations”, Math. Z., 183 (1983), 311–341 | MR | Zbl

[9] J. Kačur, “On a solution of degenerate elliptic-parabolic systems in Orlicz-Sobolev spaces. I”, Math. Z., 203 (1990), 153–171 | MR | Zbl