## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Semilinear hyperbolic functional differential problem on a cylindrical domain

W. Czernous

#### 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

https://projecteuclid.org/euclid.bbms/1331153404

Digital Object Identifier
doi:10.36045/bbms/1331153404

Mathematical Reviews number (MathSciNet)
MR2952791

Zentralblatt MATH identifier
1238.35169

#### 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