Journal of the Mathematical Society of Japan

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

Angelo FAVINI, Alfredo LORENZI, and Hiroki TANABE

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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.

Article information

Source
J. Math. Soc. Japan Volume 61, Number 1 (2009), 133-176.

Dates
First available in Project Euclid: 9 February 2009

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

Subjects
Primary: 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]
Secondary: 35K65: Degenerate parabolic equations 45D05: Volterra integral equations [See also 34A12]

Keywords
degenerate integrodifferential parabolic equations Robin boundary conditions multivalued operators analytic semigroups fundamental solutions

Citation

FAVINI, Angelo; LORENZI, Alfredo; TANABE, Hiroki. Degenerate integrodifferential equations of parabolic type with Robin boundary conditions: L 2 -theory. Journal of the Mathematical Society of Japan 61 (2009), no. 1, 133--176. doi:10.2969/jmsj/06110133. http://projecteuclid.org/euclid.jmsj/1234189031.


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References

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