Results 31 to 40 of about 602 (72)
Journal of Inequalities and Applications, 2013 This paper deals with the initial boundary value problem for a class of nonlinear Kirchhoff-type equation with dissipative term utt−φ(∥∇u∥22)Δu+a|ut|α−2ut=b|u|β−2u,x∈Ω,t>0 in a bounded domain, where a,b>0 and α,β>2 are constants.
Y. Ye
semanticscholar +2 more sources
, 2012 In this paper we consider a viscoelastic wave equation with a time-varying delay term, the coefficient of which is not necessarily positive. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we establish a general ...
Abdallah C. +7 more
core +1 more source
Decay of solutions of a system of nonlinear Klein‐Gordon equations
International Journal of Mathematics and Mathematical Sciences, Volume 9, Issue 3, Page 471-483, 1986., 1986 We study the asymptotic behavior in time of the solutions of a system of nonlinear Klein‐Gordon equations. We have two basic results: First, in the L∞(ℝ3) norm, solutions decay like 0(t−3/2) as t → +∞ provided the initial data are sufficiently small. Finally we prove that finite energy solutions of such a system decay in local energy norm as t → +∞.
José Ferreira, Gustavo Perla Menzala
wiley +1 more source
Bounded solutions for the nonlinear wave equation
Boundary Value Problems, 2013 We investigate the number of periodic weak solutions for the wave equation with nonlinearity decaying at the origin. We get a theorem which shows the existence of a bounded weak solution for this problem.
Tacksun Jung, Q. Choi
semanticscholar +2 more sources
Kirchhoff equations from quasi-analytic to spectral-gap data
, 2010 In a celebrated paper (Tokyo J. Math. 1984) K. Nishihara proved global existence for Kirchhoff equations in a special class of initial data which lies in between analytic functions and Gevrey spaces.
Ghisi, Marina, Gobbino, Massimo
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On cavitation in Elastodynamics [PDF]
, 2012 Motivated by the works of Ball (1982) and Pericak-Spector and Spector (1988), we investigate singular solutions of the compressible nonlinear elastodynamics equations.
Giesselmann, Jan +1 more
core
Journal of Function Spaces, Volume 2024, Issue 1, 2024.In this work, we deal with a fourth‐order parabolic equation with variable exponent logarithmic nonlinearity. We obtain the global existence and blowup solutions using the energy functional and potential well method.
Gülistan Butakın +3 more
wiley +1 more source
Boundary Value Problems, 2012 We investigate the degenerate Kirchhoff equations with strong damping and source terms of the form εutt−∥∇u∥22γΔu−Δut=f(u), in a bounded domain. We obtain the optimal decay rate for ∥∇ut∥22 by deriving its decay estimate from below, provided that ...
Shun-Tang Wu
semanticscholar +2 more sources
Advances in Nonlinear Analysis, 2017 We consider a second-order equation with a linear “elastic” part and a nonlinear damping term depending on a power of the norm of the velocity. We investigate the asymptotic behavior of solutions, after rescaling them suitably in order to take into ...
Ghisi Marina +2 more
doaj +1 more source
Harmonic coordinates in the string and membrane equations
, 2010 In this note, we first show that the solutions to Cauchy problems for two versions of relativistic string and membrane equations are diffeomorphic. Then we investigate the coordinates transformation presented in Ref. [9] (see (2.20) in Ref.
Chun-Lei He +2 more
core +1 more source