### Degenerate integrodifferential equations of parabolic type with Robin boundary conditions: $\bm{L^2}$ -theory

Angelo FAVINI, Alfredo LORENZI, and Hiroki TANABE
Source: J. Math. Soc. Japan Volume 61, Number 1 (2009), 133-176.

#### Abstract

This paper is devoted to solving a degenerate parabolic integrodifferential equation with the Robin boundary condition. We begin with solving the equation without the integral delay term. For that purpose we introduce some new unknown function following Favini and Yagi [4] and construct the fundamental solution to the equation to be satisfied by it by the method of Kato and Tanabe [5]. Using this fundamental solution we transform the original problem to an easily solvable integral equation for the time derivative of the new unknown function.

First Page:
Primary Subjects: 45K05
Secondary Subjects: 35K65, 45D05
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1234189031
Digital Object Identifier: doi:10.2969/jmsj/06110133
Mathematical Reviews number (MathSciNet): MR2272874
Zentralblatt MATH identifier: 05530294

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