Existence and blow up of solutions for a Petrovsky equation with variable-exponents

• Taklit Hamadouche ^[1]
  1. [1] ESTIN Engineer School in Computer Science and Digital Technologies, Amizour, Bejaia
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 80, Nº. 3, 2023, págs. 393-413
• Idioma: inglés
• DOI: 10.1007/s40324-022-00302-4
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• Resumen

  • In this paper, we consider the following nonlinear Petrovsky equation with variable exponents:

    utt + 2u + a|ut|m(.)−2ut = b|u|p(.)−2u, where a, b are positive constants and the exponents m(x), p(x) are given functions. By using the Faedo-Galerkin method, the existence of a unique weak solution is established under suitable assumptions on the variable exponents m and p. We also prove a finite-time blow-up result for arbitrary negative initial energy.