Global existence and asymptotic behavior of solutions for nonlinear parabolic equations on unbounded domains. (English) Zbl 1112.35097
The paper deals with existence and the asymptotic behavior of positive solutions for the parabolic equation \(a\Delta u - {\partial\over\partial t}u+V u^p=0\) on \(D\times(0,\infty),\) where \(a>0,\) \(D\) is a some unbounded domain in \({\mathbb R}^n\), \(n\geq 3\) and \(V\) belongs to a new parabolic class \(J^\infty\) of singular potentials generalizing the well-known Kato class at infinity \(P^\infty\) introduced recently by Zhang.
Reviewer: Lubomira Softova (Bari)
MSC:
| 35K55 | Nonlinear parabolic equations |
| 35J60 | Nonlinear elliptic equations |
| 35B40 | Asymptotic behavior of solutions to PDEs |
Keywords:
parabolic equation; elliptic equation; Green function; positive solution; Schauder fixed point theorem; asymptotic behaviorReferences:
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