A wave equation with discontinuous time delay
International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 4, Page 781-788, 1992., 1992 The influence of certain discontinuous delays on the behavior of the solutions of the wave equation is studied.
Joseph Wiener, Lokenath Debnath
wiley +1 more source
Blow-up of solutions for Euler-Bernoulli equation with nonlinear time delay
Open MathematicsWe study the Euler-Bernoulli equations with time delay: utt+Δ2u−g1∗Δ2u+g2∗Δu+μ1ut(x,t)∣ut(x,t)∣m−2+μ2ut(x,t−τ)∣ut(x,t−τ)∣m−2=f(u),{u}_{tt}+{\Delta }^{2}u-{g}_{1}\ast {\Delta }^{2}u+{g}_{2}\ast \Delta u+{\mu }_{1}{u}_{t}\left(x,t){| {u}_{t}\left(x,t ...
Lin Rongrui, Gao Yunlong, She Lianbing
doaj +1 more source
The global solution and blow-up phenomena to a modified Novikov equation
, 2014 A modified Novikov equation with symmetric coefficients is investigated. Provided that the initial value u0∈Hs(R) (s>32), (1−∂x2)u0 does not change sign and the solution u itself belongs to L1(R), the existence and uniqueness of the global strong ...
S. Lai, Haibo Yan, Nan Li
semanticscholar +1 more source
Limiting behavior of quasilinear wave equations with fractional-type dissipation
Advanced Nonlinear StudiesIn this work, we investigate a class of quasilinear wave equations of Westervelt type with, in general, nonlocal-in-time dissipation. They arise as models of nonlinear sound propagation through complex media with anomalous diffusion of Gurtin–Pipkin type.
Kaltenbacher Barbara +2 more
doaj +1 more source
Electromagnetic source localization with finite set of frequency measurements [PDF]
, 2014 A phase conjugation algorithm for localizing an extended radiating electromagnetic source from boundary measurements of the electric field is presented. Measurements are taken over a finite number of frequencies.
Anjum, Saman +3 more
core
Global attractors for the one dimensional wave equation with displacement dependent damping
, 2010 We study the long-time behavior of solutions of the one dimensional wave equation with nonlinear damping coefficient. We prove that if the damping coefficient function is strictly positive near the origin then this equation possesses a global ...
Arrietta +10 more
core +1 more source
Spatial estimates for a class of hyperbolic equations with nonlinear dissipative boundary conditions
Boundary Value Problems, 2011 This paper is concerned with investigating the spatial behavior of solutions for a class of hyperbolic equations in semi-infinite cylindrical domains, where nonlinear dissipative boundary conditions imposed on the lateral surface of the cylinder.
Tahamtani Faramarz, Peyravi Amir
doaj
General decay for a wave equation of Kirchhoff type with a boundary control of memory type
, 2011 A nonlinear wave equation of Kirchhoff type with memory condition at the boundary in a bounded domain is considered. We establish a general decay result which includes the usual exponential and polynomial decay rates.
Shun-Tang Wu
semanticscholar +1 more source
A few remarks on the generalized Novikov equation
, 2013 This paper deals with the Cauchy problem for a generalized Novikov equation ut−uxxt+(b+1)u2ux=buuxuxx+u2uxxx, where b is a constant. The local well-posedness in the critical Besov space B2,13/2 is established.
Shouming Zhou, Rong Chen
semanticscholar +1 more source
Solitary wave solutions of the delayed KP–BBM equation
Advances in Nonlinear AnalysisIn this paper, a type of shallow water wave model referred to as the Kadomtsev–Petviashvili–Benjamin–Bona–Mahony (KP–BBM) equation is studied. Initially, the unperturbed form of the KP–BBM equation is examined.
Xia Yonghui, Zhang Haojie, Zheng Hang
doaj +1 more source