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RESEARCH PRODUCT
Global Existence for Nonlinear Parabolic Problems With Measure Data– Applications to Non-uniqueness for Parabolic Problems With Critical Gradient terms
Boumediene AbdellaouiSergio Segura De LeónAndrea Dall'aglioIreneo Peralsubject
010101 applied mathematicsNonlinear systemGeneral Mathematics010102 general mathematicsMathematical analysisNon uniquenessStatistical and Nonlinear Physics0101 mathematics01 natural sciencesMeasure (mathematics)MathematicsVolume (compression)description
Abstract In the present article we study global existence for a nonlinear parabolic equation having a reaction term and a Radon measure datum: where 1 < p < N, Ω is a bounded open subset of ℝN (N ≥ 2), Δpu = div(|∇u|p−2∇u) is the so called p-Laplacian operator, sign s ., ϕ(ν0) ∈ L1(Ω), μ is a finite Radon measure and f ∈ L∞(Ω×(0, T)) for every T > 0. Then we apply this existence result to show wild nonuniqueness for a connected nonlinear parabolic problem having a gradient term with natural growth.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-11-01 | Advanced Nonlinear Studies |