On an Integral Inequality with a Kernel Singular in Time and Space

Volume 4, Issue 4, 2003

Article 82

ON AN INTEGRAL INEQUALITY WITH A KERNEL SINGULAR IN TIME AND SPACE

NASSER-EDDINE TATAR

KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS
DEPARTMENT OF MATHEMATICAL SCIENCES
DHAHRAN 31261, SAUDI ARABIA.
E-Mail: tatarn@kfupm.edu.sa

Received 07 March, 2003; Accepted 01 August, 2003.
Communicated by: D. Bainov

ABSTRACT. In this paper we deal with a nonlinear singular integral inequality which arises in the study of partial differential equations. The integral term is non local in time and space and the kernel involved is also singular in both the time and the space variable. The estimates we prove may be used to establish (global) existence and asymptotic behavior results for solutions of the corresponding problems.

Key words:
Nonlinear integral inequality, Singular kernel.

2000 Mathematics Subject Classification:
42B20, 26D07, 26D15.

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