Existence, asymptotic behaviour, and blow up of solutions for a class of nonlinear wave equations with dissipative and dispersive terms

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Polat N., KAYA D.

Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences, cilt.64, sa.5-6, ss.315-326, 2009 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 64 Sayı: 5-6
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1515/zna-2009-5-605
  • Dergi Adı: Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.315-326
  • Anahtar Kelimeler: Asymptotic behaviour, Blow up of solutions, Global solution, Initial boundary value problem, Nonlinear wave equation
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

We consider the existence, both locally and globally in time, the asymptotic behaviour, and the blow up of solutions to the initial boundary value problem for a class of nonlinear wave equations with dissipative and dispersive terms. Under rather mild conditions on the nonlinear term and the initial data we prove that the above-mentioned problem admits a unique local solution, which can be continued to a global solution, and the solution decays exponentially to zero as t → +∞. Finally, under a suitable condition on the nonlinear term, we prove that the local solutions with negative and nonnegative initial energy blow up in finite time. © 2009 Verlag der Zeitschrift für Naturforschung, Tübingen.