Global Existence for Nonlinear Parabolic Problems With Measure Data– Applications to Non-uniqueness for Parabolic Problems With Critical Gradient terms-Reference-Cited by-同舟云学术

Global Existence for Nonlinear Parabolic Problems With Measure Data– Applications to Non-uniqueness for Parabolic Problems With Critical Gradient terms

Published:2011-11-01 Issue:4 Volume:11 Page:733-780
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Abdellaoui Boumediene¹,Dall’Aglio Andrea²,Peral Ireneo³,Léon Sergio Segura de⁴

Affiliation:

1. Département de Mathématiques, Université Abou Bakr Belkaïd, Tlemcen Tlemcen 13000, Algeria

2. Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza” Piazzale A. Moro 2, I-00185 Roma , Italy

3. Departamento de Matemáticas, Universidad Autonoma de Madrid Cantoblanco 28049 Madrid, Spain

4. Departament d’Anàlisi Matemàtica, Universitat de València Dr. Moliner 50, 46100 Burjassot, Valencia, Spain

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2011-0401/pdf

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