6533b7d9fe1ef96bd126c19c
RESEARCH PRODUCT
Parabolic equations with nonlinear singularities
Pedro J. Martínez-aparicioFrancesco Petittasubject
asymptotic behavior; nonlinear parabolic equations; singular parabolic equationsApplied MathematicsMathematical analysisnonlinear parabolic equationsLower ordersingular parabolic equationsParabolic partial differential equationNonlinear parabolic equationsNonlinear systemGravitational singularityasymptotic behaviorSingular equationU-1AnalysisMathematicsMathematical physicsdescription
Abstract We show the existence of positive solutions u ∈ L 2 ( 0 , T ; H 0 1 ( 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 { u t − Δ u + u 1 − u = f ( x , t ) in Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in Ω , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , and quasilinear problems having natural growth with respect to the gradient, whose model is { u t − Δ u + ∣ ∇ u ∣ 2 u γ = f ( x , t ) in Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in Ω , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , with γ > 0 . Moreover, we prove a comparison principle and, as an application, we study the asymptotic behavior of the solution as t goes to infinity.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-01-01 | Nonlinear Analysis: Theory, Methods & Applications |