Article ID Journal Published Year Pages File Type
841486 Nonlinear Analysis: Theory, Methods & Applications 2011 18 Pages PDF
Abstract

We show the existence of positive solutions u∈L2(0,T;H01(Ω)) for nonlinear parabolic problems with singular lower order terms of the asymptote-type. More precisely, we shall consider both semilinear problems whose model is {ut−Δu+u1−u=f(x,t)inΩ×(0,T),u(x,0)=u0(x)inΩ,u(x,t)=0on∂Ω×(0,T), and quasilinear problems having natural growth with respect to the gradient, whose model is {ut−Δu+∣∇u∣2uγ=f(x,t)inΩ×(0,T),u(x,0)=u0(x)inΩ,u(x,t)=0on∂Ω×(0,T), with γ>0γ>0. Moreover, we prove a comparison principle and, as an application, we study the asymptotic behavior of the solution as tt goes to infinity.

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Physical Sciences and Engineering Engineering Engineering (General)
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