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| A BLOW-UP RESULT FOR A CLASS DOUBLY NONLINEAR PARABOLIC EQUATIONS WITH VARIABLE-EXPONENT NONLINEARITIES |
| Qingying Hu,Donghao Li,Hongwei Zhang |
| (Dept. of Math., Henan University of Technology,Zhengzhou 450001, Henan, PR China) |
| DOI： |
| Abstract: |
| This paper deals with the following doubly nonlinear parabolic equations (u+|u|^{r(x)-2}u)_t-{\rm div}(|\nabla u|^{m(x)-2}\nabla u)=|u|^{p(x)-2} u, where the exponents of
nonlinearity $r(x),m(x)$ and $p(x)$ are given functions. Under some appropriate assumptions on the exponents of nonlinearity, and with certain initial data, a blow-up result is established with positive initial energy. |
| Key words: doubly nonlinear parabolic equations; variable-exponent nonlinearities; blow-up |