A singular parabolic equation with logarithmic nonlinearity and L-p-initial data

Author(s)

Ferreira, Lucas C. F. ^[1] ; de Queiroz, Olivaine S. ^[1]

Affiliation

^[1] Univ Estadual Campinas, IMECC, Dept Matemat, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: Journal of Differential Equations; v. 249, n. 2, p. 349-365, JUL 15 2010.
• Web of Science Citations: 4

Abstract

We study a parabolic equation with logarithmic nonlinearity and homogeneous Dirichlet condition in a smooth bounded domain. We firstly prove a result about existence of positive solutions with initial data in L(p)-spaces, 1 < p < infinity; in order to overcome the singular logarithmic nonlinearity, among other arguments, we employ Hardy's inequality. After, the life span of the obtained solutions is studied. In particular we show a connection between global existence and solutions of the associated elliptic problem. (C) 2010 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 08/04737-0 - Equations in Singular Spaces and Optimal Mass Transportation
• Grantee: Lucas Catão de Freitas Ferreira
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 08/01458-2 - Partial differential equations and curvature flows
• Grantee: Olivâine Santana de Queiroz
• Support Opportunities: Scholarships in Brazil - Post-Doctoral