Geodesic
Existence theorems for solutions of parabolic equations with variable order of nonlinearity
Informatics and Automation, Differential equations and dynamical systems, Tome 270 (2010), pp. 21-32

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

We study the solvability of an initial-boundary value problem for second-order parabolic equations with variable order of nonlinearity. In the model case, the equation contains the $p$-Laplacian with a variable exponent $p(x,t)$. We prove that if the measurable exponent $p$ is separated from unity and infinity, then the problem has $W$- and $H$-solutions. 
@article{TRSPY_2010_270_a1,
     author = {Yu. A. Alkhutov and V. V. Zhikov},
     title = {Existence theorems for solutions of parabolic equations with variable order of nonlinearity},
     journal = {Informatics and Automation},
     pages = {21--32},
     publisher = {mathdoc},
     volume = {270},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2010_270_a1/}
}
TY  - JOUR
AU  - Yu. A. Alkhutov
AU  - V. V. Zhikov
TI  - Existence theorems for solutions of parabolic equations with variable order of nonlinearity
JO  - Informatics and Automation
PY  - 2010
SP  - 21
EP  - 32
VL  - 270
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2010_270_a1/
LA  - ru
ID  - TRSPY_2010_270_a1
ER  - 
%0 Journal Article
%A Yu. A. Alkhutov
%A V. V. Zhikov
%T Existence theorems for solutions of parabolic equations with variable order of nonlinearity
%J Informatics and Automation
%D 2010
%P 21-32
%V 270
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2010_270_a1/
%G ru
%F TRSPY_2010_270_a1
Yu. A. Alkhutov; V. V. Zhikov. Existence theorems for solutions of parabolic equations with variable order of nonlinearity. Informatics and Automation, Differential equations and dynamical systems, Tome 270 (2010), pp. 21-32. http://geodesic.mathdoc.fr/item/TRSPY_2010_270_a1/