Results 21 to 30 of about 526 (46)

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

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
core   +1 more source

Blowup and Global Solutions of a Fourth‐Order Parabolic Equation With Variable Exponent Logarithmic Nonlinearity

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, Erhan Pişkin, Ercan Çelik, Shrideh K. Q. Al-Omari   +3 more
wiley   +1 more source

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, Tzavaras, Athanasios E.   +1 more
core  

Quantization of energy and weakly turbulent profiles of solutions to some damped second-order evolution equations

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, Gobbino Massimo, Haraux Alain   +2 more
doaj   +1 more source

Exponential energy decay of solutions for a system of viscoelastic wave equations of Kirchhoff type with strong damping

, 2011
The initial boundary value problem for a system of viscoelastic wave equations of Kirchhoff type with strong damping is considered. We prove that, under suitable assumptions on relaxation functions and certain initial data, the decay rate of the ...
Agre K, Andrade D, Gang Li, Komornik V, Li M-R, Liang F, Linghui Hong, Munoz Rivera JE, Park JY, Said-Houari B, Santos ML, Vicente A, Wenjun Liu, Wu S-T, Wu S-T   +14 more
core   +1 more source

Integrable Systems and Metrics of Constant Curvature

, 2001
In this article we present a Lagrangian representation for evolutionary systems with a Hamiltonian structure determined by a differential-geometric Poisson bracket of the first order associated with metrics of constant curvature.
Dubrovin B.A., Faddeev L.D., Ferapontov E V, Ferapontov E V, Mokhov O I, Mokhov O.I., Pavlov Maxim V., Pavlov Maxim V., Tsarev S.P.   +8 more
core   +1 more source

A Remark on Unconditional Uniqueness in the Chern-Simons-Higgs Model [PDF]

, 2013
The solution of the Chern-Simons-Higgs model in Lorenz gauge with data for the potential in $H^{s-1/2}$ and for the Higgs field in $H^s \times H^{s-1}$ is shown to be unique in the natural space $C([0,T];H^{s-1/2} \times H^s \times H^{s-1})$ for $s \ge 1$
Daniel, Oliveira Da Silva, Sigmund Selberg   +2 more
core  

Simple Non Linear Klein-Gordon Equations in 2 space dimensions, with long range scattering

, 2007
We establish that solutions, to the most simple NLKG equations in 2 space dimensions with mass resonance, exhibits long range scattering phenomena. Modified wave operators and solutions are constructed for these equations.
E. Taflin, Erik Taflin, H. Lindblad, H. Lindblad, J. Ginibre, J.C.H. Simon, J.C.H. Simon, J.M. Delort, L. Hörmander, M. Flato, M. Flato, T. Ozawa   +11 more
core   +1 more source

Mathematical model of the impact of chemotherapy and antiangiogenic therapy on drug resistance in glioma growth

Computational and Mathematical Biophysics
This study presents a mathematical model of glioma growth dynamics with drug resistance, capturing interactions among five cell populations – glial cells, sensitive and resistant glioma cells, endothelial cells, and neurons – alongside chemotherapy and ...
Hanum Latifah, Susyanto Nanang, Ertiningsih Dwi   +2 more
doaj   +1 more source