Yaojun Ye, "Existence and Longtime Behavior of Global Solutions for a Nonlinear Damping Petrovsky Equation," WSEAS Transactions on Mathematics, vol. 13, pp. 547-556, 2014, DOI:
Yaojun Ye. Existence and Longtime Behavior of Global Solutions for a Nonlinear Damping Petrovsky Equation.
WSEAS Transactions on Mathematics. 2014;13:547-556.
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 13, 2014
Existence and Longtime Behavior of Global Solutions for a Nonlinear Damping Petrovsky Equation
Author:
Abstract: The initial boundary value problem for a class of nonlinearly damped Petrovsky equation utt + Δ2u + a(1 + |ut|r)ut = b|u|pu in a bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set in H2 0 (Ω), and obtain the energy decay result through the use of an important lemma of V.Komornik. Meanwhile, under the conditions of the positive initial energy, it is proved that the solution blows up in the finite time and the lifespan estimates of solutions are also given.
Pages: 547-556 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 13, 2014, Art. #53 DOI: *As the DOI is a unique identifier, it is already available in the pdf version.
**The DOI link will be activated in the first midst of January 2026.
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