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Blow up for the wave equation with a fractional damping

Alaimia M. R., Tatar N.-E.

Journal of Applied Analysis

2005

Vol. 11, nr 1

133-144

We consider the wave equation with a fractional damping of order between o and 1 and a polynomial source. Introducing a new functional and using an argument due to Georgiev and Todorova [1] together with some appropriate estimates, it is proved that some solutions blow up in finite time.

On the wave equations with a dissipation anda source of cubic convolution type in Rn

Tatar N.-e.

Demonstratio Mathematica

2004

Vol. 37, nr 3

543--555

We study the interaction between a dissipative term and a source term of cubic convolution type for the wave equation in Rn. These terms have both the same form and involve convolutions with a singular kernel. The investigation will depend on the coefficient of the source term which is a functions of the time variable. Some results on the boundedness of the solutions are proved. Moreover, we establish an asymptotic stability result.

On the Aronszajn property for an integral equation with weakly singular kernel

Szufla S.

Demonstratio Mathematica

2004

Vol. 37, nr 1

133--136

Solution of Fredholm integral of first kind Singular Kernel

El-Bary A.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2000

z. 24 [181]

27-35

This paper is devoted to give and discuss the method of solving the Fredholm integral equation of the first kind with singular kernel by using the Fourier method.