| Autor: |
Guo, Bin, Zhang, Jingjing, Liao, Menglan |
| Rok vydání: |
2020 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
The aim of this paper is to apply the modified potential well method and some new differential inequalities to study the asymptotic behavior of solutions to the initial homogeneous $\hbox{Neumann}$ problem of a nonlinear diffusion equation driven by the $p(x)$-\hbox{Laplace} operator. Complete classification of global existence and blow-up in finite time of solutions is given when the initial data satisfies different conditions. Roughly speaking, we obtain a threshold result for the solution to exist globally or to blow up in finite time when the initial energy is subcritical and critical, respectively. Further, the decay rate of the $L^2$ norm is also obtained for global solutions. Sufficient conditions for the existence of global and blow-up solutions are also provided for supercritical initial energy. At last, we give two-sided estimates of asymptotic behavior when the diffusion term dominates the source. This is a continuation of our previous work \cite{GG}. |
| Databáze: |
arXiv |
| Externí odkaz: |
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