Results 21 to 30 of about 82 (81)
Mathematical Problems in Engineering, Volume 2004, Issue 3, Page 185-195, 2004., 2004 This paper presents an integral solution of the generalized one‐dimensional equation of energy transport with the convective term.The solution of the problem has been achieved by the use of a novel technique that involves generalized derivatives (in particular, derivatives of noninteger orders).
Vladimir V. Kulish
wiley +1 more source
New singular solutions of Protter′s problem for the 3D wave equation
Abstract and Applied Analysis, Volume 2004, Issue 4, Page 315-335, 2004., 2004 In 1952, for the wave equation,Protter formulated some boundary value problems (BVPs), which are multidimensional analogues of Darboux problems on the plane. He studied these problems in a 3D domain Ω0, bounded by two characteristic cones Σ1 and Σ2,0 and a plane region Σ0. What is the situation around these BVPs now after 50 years?
M. K. Grammatikopoulos +2 more
wiley +1 more source
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
doaj +1 more source
Mathematical Problems in Engineering, Volume 2003, Issue 4, Page 173-179, 2003., 2003 The relationship between the local temperature and the local heat flux has been established for the homogeneous hyperbolic heat equation. This relationship has been written in the form of a convolution integral involving the modified Bessel functions.
Vladimir V. Kulish, Vasily B. Novozhilov
wiley +1 more source
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
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. +4 more
doaj +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
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
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