Geodesic
Existence and uniqueness of solutions for a quasilinear evolution equation in an Orlicz space
Zheng Zhou1 ; Fei Fang2
1School of Applied Mathematical Sciences Xiamen University of Technology Xiamen 361024, China
2Department of Mathematics Beijing Technology and Business University Beijing 100048, China
Annales Polonici Mathematici, Tome 117 (2016) no. 3, pp. 269-289
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We consider the following quasilinear evolution equation in an Orlicz space: $$ u_t=\mathrm {div}(a(|\nabla u|)\nabla u)+f(x,t,u), $$ where $a\in C^1(\mathbb {R})$ and $f\in C^1(\overline {\varOmega }\times [0,T]\times \mathbb {R})$. We use the difference method to transform the evolution problem to a sequence of elliptic problems. Then by making some uniform estimates for these elliptic problems, we obtain the existence of global solutions for the evolution problem. Uniqueness is also proved.
DOI : 10.4064/ap3861-4-2016
Keywords: consider following quasilinear evolution equation orlicz space mathrm div nabla nabla u where mathbb overline varomega times times mathbb difference method transform evolution problem sequence elliptic problems making uniform estimates these elliptic problems obtain existence global solutions evolution problem uniqueness proved

Zheng Zhou  1   ; Fei Fang  2

1 School of Applied Mathematical Sciences Xiamen University of Technology Xiamen 361024, China
2 Department of Mathematics Beijing Technology and Business University Beijing 100048, China 
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Zheng Zhou; Fei Fang. Existence and uniqueness of solutions for a quasilinear evolution equation in an Orlicz space. Annales Polonici Mathematici, Tome 117 (2016) no. 3, pp. 269-289. doi: 10.4064/ap3861-4-2016

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