Bulletin of the Belgian Mathematical Society - Simon Stevin

Semilinear hyperbolic functional differential problem on a cylindrical domain

W. Czernous

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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

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

First available in Project Euclid: 7 March 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Carathéodory solutions global existence characteristics uniform cone condition


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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