Results 31 to 40 of about 1,175 (77)

LONG TIME BEHAVIOR OF THE SOLUTIONS OF NLW ON THE $d$-DIMENSIONAL TORUS

Forum of Mathematics, Sigma, 2020
We consider the nonlinear wave equation (NLW) on the $d$-dimensional torus $\mathbb{T}^{d}$ with a smooth nonlinearity of order at least 2 at the origin. We prove that, for almost any mass, small and smooth solutions of high Sobolev indices are stable up
JOACKIM BERNIER, ERWAN FAOU, BENOÎT GRÉBERT   +2 more
doaj   +1 more source

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, Babin, Belleri, Gatti, Ghidaglia, Ladyzhenskaya, Lions, Pata, Pata, Pata, Temam   +10 more
core   +1 more source

An inverse problem for a nonlinear Schrödinger equation

Abstract and Applied Analysis, Volume 7, Issue 7, Page 385-399, 2002., 2002
We study the dependence on the control q of the interval of definition of the solution u of the Cauchy problem ιu′ + Δ u = −λ|u| 2u − ιqu in ℝ 2 × (0, T), u(x, 0) = ω in ℝ 2, and we prove a version of Fibich′s conjecture. Feedback laws for an inverse problem of the above equation with experimental data, measured on a portion of the boundary of an open,
Bui An Ton
wiley   +1 more source

Study of exponential stability of coupled wave systems via distributed stabilizer

International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 8, Page 479-491, 2001., 2001
Stabilization of the system of wave equations coupled in parallel with coupling distributed springs and viscous dampers are under investigation due to different boundary conditions and wave propagation speeds. Numerical computations are attempted to confirm the theoretical results.
Mahmoud Najafi
wiley   +1 more source

Uniform stabilization for a strongly coupled semilinear/linear system

Advanced Nonlinear Studies, 2022
In this manuscript, we analyze the exponential stability of a strongly coupled semilinear system of Klein-Gordon type, posed in an inhomogeneous medium Ω\Omega , subject to local dampings of different natures distributed around a neighborhood of the ...
Cavalcanti Marcelo M., Domingos Cavalcanti Valéria N., Almeida Júnior Dilberto da Silva, Gonzalez Martinez Victor Hugo, Santos Mauro de Lima   +4 more
doaj   +1 more source

On closed‐form solutions of some nonlinear partial differential equations

International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 2, Page 81-88, 2000., 2000
This paper is devoted to closed‐form solutions of the partial differential equation: θxx + θyy + δexp(θ) = 0, which arises in the steady state thermal explosion theory. We find simple exact solutions of the form θ(x, y) = Φ(F(x) + G(y)), and θ(x, y) = Φ(f(x + y) + g(x − y)). Also, we study the corresponding nonlinear wave equation.
S. S. Okoya
wiley   +1 more source

Well-posedness of damped Kirchhoff-type wave equation with fractional Laplacian

Advanced Nonlinear Studies
In the present paper, we study the well-posedness of the solution to the initial boundary value problem for the damped Kirchhoff-type wave equation with fractional Laplacian.
Chen Shaohua, Han Jiangbo, Xu Runzhang, Yang Chao, Zhang Meina   +4 more
doaj   +1 more source

Random attractors for stochastic retarded strongly damped wave equations with additive noise on bounded domains

Open Mathematics, 2019
In this paper we study the asymptotic behavior for a class of stochastic retarded strongly damped wave equation with additive noise on a bounded smooth domain in ℝd. We get the existence of the random attractor for the random dynamical systems associated
Jia Xiaoyao, Ding Xiaoquan
doaj   +1 more source

Observability and uniqueness theorem for a coupled hyperbolic system

International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 6, Page 423-432, 2000., 2000
We deal with the inverse inequality for a coupled hyperbolic system with dissipation. The inverse inequality is an indispensable inequality that appears in the Hilbert Uniqueness Method (HUM), to establish equivalence of norms which guarantees uniqueness and boundary exact controllability results.
Boris V. Kapitonov, Joel S. Souza
wiley   +1 more source

Asymptotic parabolicity for strongly damped wave equations

, 2013
For $S$ a positive selfadjoint operator on a Hilbert space, \[ \frac{d^2u}{dt}(t) + 2 F(S)\frac{du}{dt}(t) + S^2u(t)=0 \] describes a class of wave equations with strong friction or damping if $F$ is a positive Borel function.
Fragnelli, Genni, Goldstein, Gisèle Ruiz, Goldstein, Jerome A., Romanelli, Silvia   +3 more
core   +1 more source