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Blow-up of solutions of a non-linear wave equation with fractional damping and infinite memory
  • Mokhtar Kirane,
  • Aounallah Radhouane
Mokhtar Kirane
Khalifa University

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Aounallah Radhouane
Universite Djillali Liabes de Sidi Bel Abbes
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We consider a non-linear wave equation with an internal fractional damping, a polynomial source and an infinite memory. Using the semi-group theory, we get the existence of a local weak solution. Moreover, we show under some conditions, local solutions may blow up a in finite time; this is achieved by constructing a suitable Lyapunov functional.