Bulletin of the Belgian Mathematical Society - Simon Stevin

Semilinear hyperbolic functional differential problem on a cylindrical domain

W. Czernous

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Abstract

We consider the initial boundary value problem for a semi-linear partial functional differential equation of the first order on a cylindrical domain in $n+1$ dimensions. Projection of the domain onto the $n$-dimensional hyperplane is a connected set with boundary satisfying certain type of cone condition. Using the method of characteristics and the Banach contraction theorem, we prove the global existence, uniqueness and continuous dependence on data of Carathéodory solutions of the problem. This approach cover equations with deviating variables as well as differential integral equations.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 1 (2012), 1-17.

Dates
First available in Project Euclid: 7 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1331153404

Digital Object Identifier
doi:10.36045/bbms/1331153404

Mathematical Reviews number (MathSciNet)
MR2952791

Zentralblatt MATH identifier
1238.35169

Subjects
Primary: 35R10: Partial functional-differential equations 35A30: Geometric theory, characteristics, transformations [See also 58J70, 58J72] 35A01: Existence problems: global existence, local existence, non-existence

Keywords
Carathéodory solutions global existence characteristics uniform cone condition

Citation

Czernous, W. Semilinear hyperbolic functional differential problem on a cylindrical domain. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 1, 1--17. doi:10.36045/bbms/1331153404. https://projecteuclid.org/euclid.bbms/1331153404


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