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Some existence results for a nonlocal non-isotropic problem

Bentifour Rachid, Miri Sofiane El-Hadi

Opuscula Mathematica

2021

Vol. 41, no. 1

5--23

In this paper we deal with the following problem [formula] where Ω is a bounded regular domain in RN . We will assume without loss of generality that [formula] PN and that ƒ and g are non-negative functions belonging to a suitable Lebesgue space [formula].

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.