Journal of Applied Analysis 11 (2005), No. 1, 133--144
Copyright Heldermann Verlag 2005
Blow Up for the Wave Equation with a Fractional Damping
Mohamed Ridha Alaimia
King Fahd University of Petroleum and Minerals, Department of Mathematical Sciences, Dhahran 31261, Saudi Arabia
alaimia@kfupm.edu.sa
Nasser-Eddine Tatar
King Fahd University of Petroleum and Minerals, Department of Mathematical Sciences, Dhahran 31261, Saudi Arabia
tatarn@kfupm.edu.sa
We consider the wave equation with a fractional damping of order between 0 and 1 and a polynomial source. Introducing a new functional and using an argument due to V. Georgiev and G. Todorova [J. Differential Equations 109 (1994) 295--308] together with some appropriate estimates, it is proved that some solutions blow up in finite time.
Keywords: Blow up, Caputo's fractional derivative, integro-differential problem, modified energy functional, singular kernel.
MSC: 35L20, 35L70, 35B05
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