Abstract
In this work, we consider a class of initial boundary value problems for fourth-order dispersive wave equations with superlinear damping and non-local source terms as well as time-dependent coefficients in Ω×(t>0), where Ω is a bounded domain in RN and N≥2. We prove that there exists a safe time interval of existence in the solution [0,T], with T being a lower bound of the blowup time t*. Moreover, we find an explicit lower bound of t*, assuming the coefficients are positive constants.
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
Reference29 articles.
1. Galaktionov, A.V., Mitidieri, E.L., and Pohozaev, S.I. (2014). Monographs and Research Notes in Mathematics, CRC Press.
2. Lyapunov functions and Lp—Stimates for a class of reaction-diffusion systems;Horstmann;Colloq. Math.,2001
3. On global solution of nonlinear hyperbolic equations;Sattinger;Arch. Ration. Mech. Anal.,1968
4. Saddle points and instability on nonlinear hyperbolic equations;Payne;Isr. J. Math.,1975
5. On potential wells and vacuum isolating of solutions for semilinear wave equation;Liu;J. Differ. Equ.,2003
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