Global existence and blow-up of a Petrovsky equation with general nonlinear dissipative and source terms
DOI:
https://doi.org/10.24193/subbmath.2023.1.16Keywords:
Global existence, blow-up, nonlinear source, nonlinear dissipative, Petrovsky equation.Abstract
This work studies the initial boundary value problem for the Petrovsky equation with nonlinear damping.
Furthermore, we show that this solution blows up in a finite time when the initial energy is negative.
Mathematics Subject Classification (2010): 93C20, 93D15
Received 24 June 2020; Revised 221 July 2020. Published Online: 2023-03-20. Published Print: 2023-04-30
References
Adams, R.A, Sobolev Spaces, Academic Press, New York, 1975.
Amroun, N.E., Benaissa, A., Global existence and energy decay of solution to a Petroesky equation with general dissipation and source term, Georgian Math. J., 13(2006), no. 3, 397–410.
Dautray, R., Lions, J.L., Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques, vol. 3, Masson, Paris, 1985.
Georgiev, V., Todorova, G., Existence of a solution of the wave equation with nonlinear damping and source terms, J. Differential Equations, 109(1994), no. 2, 295–308.
Guesmia, A., Existence globale et stabilisation interne non linéaire d’un systèm de Petrovsky, Bull. Belg. Math. Soc. Simon Stevin, 5(1998), 583–594.
Li, G., Sun, Y., Liu, W., Global existence and blow-up of solutions for a strongly damped Petrovsky system with nonlinear damping, Appl. Anal., 91(2012), no. 3, 575–586.
Lions, J.L., Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod Gautier-Villars, Paris, 1969.
Lions, J.L., Magenes, E., Problèmes aux Limites Non Homogènes et Applications, vol. 1, 2. Dunod, Paris, 1968.
Messaoudi, S.A., Global existence and nonexistence in a system of Petrovsky, J. Math. Anal. Appl., 265(2002), no. 2, 296–308.
Piskin, E., Polat, N., On the decay of solutions for a nonlinear Petrovsky equation, Math. Sci. Lett., 3(2014), no. 1, 43–47.
Wenying, C., Yong, Z., Global nonexistence for a semilinear Petrovsky equation, Non-linear Anal., 70(2009), 3203–3208.
Wu, S.T., Tsai, L.Y., On global solutions and blow-up of solutions for a nonlinearly damped Petrovsky system, Taiwanese J. Math., 19(2009), no. 2A, 545–558.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
