Results 31 to 40 of about 1,145 (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 +2 more
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Method of replacing the variables for generalized symmetry of the D′Alembert equation
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 3, Page 149-155, 2002., 2002 We show that by the generalized understanding of symmetry, the D′Alembert equation for one component field is invariant with respect to arbitrary reversible coordinate transformations.
Gennadii A. Kotel′nikov
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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. +4 more
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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
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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
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Soliton and periodic wave solutions to the osmosis K(2, 2) equation
, 2009 In this paper, two types of traveling wave solutions to the osmosis K(2, 2) equation are investigated. They are characterized by two parameters.
Fan, Xinghua, Tian, Lixin, Zhou, Jiangbo
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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
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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
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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
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, 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
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