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April  2002, 8(2): 451-468. doi: 10.3934/dcds.2002.8.451

Nonlinear parabolic differential equations and inequalities

Wolfgang Walter 1,

1. 

Math. Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany

Revised  November 2001 Published  January 2002

The paper starts with a short review on the history of PDEs and their related inequalities. We present a unified approach to the basic parabolic differential inequalities. It starts in Section 2 with the famous Lemma of Nagumo and leads to recent and new result on parabolic equations with singular nonlinear elliptic operators (7) that include the p-Laplacian and the operator of capillary surfaces. Sections 3 and 4 deal with the one-dimensional case and radial solutions. A Semi-Strong Minimum Principle is found in Section 6.
Keywords: p-Laplacian., nonlinear inequalities, Minimum principles, Parabolic differential equations, radial solutions.
Mathematics Subject Classification: Primary: 35K10; Secondary: 35K2.
Citation: Wolfgang Walter. Nonlinear parabolic differential equations and inequalities. Discrete & Continuous Dynamical Systems, 2002, 8 (2) : 451-468. doi: 10.3934/dcds.2002.8.451
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