Results 11 to 20 of about 53 (49)
Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 1, Page 131-145, 1999., 1999 The Cauchy problem for the damped Boussinesq equation with small initial data is considered in two space dimensions. Existence and uniqueness of its classical solution is proved and the solution is constructed in the form of a series. The major term of its long‐time asymptotics is calculated explicitly and a uniform in space estimate of the residual ...
Vladimir V. Varlamov
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Existence of periodic traveling wave solutions to the generalized forced Boussinesq equation
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 3, Page 643-648, 1999., 1999 The generalized forced Boussinesq equation, utt − uxx + [f(u)]xx + uxxxx = h0, and its periodic traveling wave solutions are considered. Using the transform z = x − ωt, the equation is converted to a nonlinear ordinary differential equation with periodic boundary conditions.
Kenneth L. Jones, Yunkai Chen
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Nearly conconcentric Korteweg‐de Vries equation and periodic traveling wave solution
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 1, Page 183-187, 1998., 1998 The generalized nearly concentric Korteweg‐de Vries equation is considered. The author converts the equation into the power Kadomtsev‐Petviashvili equation . Solitary wave solutions and cnoidal wave solutions are obtained. The cnoidal wave solutions are shown to be representable as infinite sums of solitons by using Fourier series expansions and ...
Yunkai Chen
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Abstract and Applied Analysis, Volume 2, Issue 3-4, Page 281-299, 1997., 1997 For the damped Boussinesq equation , the second initial‐boundary value problem is considered with small initial data. Its classical solution is constructed in the form of a series in small parameter present in the initial conditions and the uniqueness of solutions is proved. The long‐time asymptotics is obtained in the explicit form and the question of
Vladimir V. Varlamov
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Conservation laws for incompressible fluids
International Journal of Mathematics and Mathematical Sciences, Volume 12, Issue 2, Page 377-384, 1989., 1989 By means of a direct approach, a complete set of conservation laws for incompressible fluids is determined. The problem is solved in the material (Lagrangian) description and the results are eventually rewritten in the spatial (Eulerian) formulation. A new infinite family of conservation laws is determined, besides those for linear momentum, angular ...
G. Caviglia, A. Morro
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On singularities of capillary surfaces in the absence of gravity
International Journal of Mathematics and Mathematical Sciences, Volume 6, Issue 1, Page 81-87, 1983., 1983 We study numerical solutions to the equation of capillary surfaces in trapezoidal domains in the absence of gravity when the boundary contact angle declines from 90° to some critical value. We also discuss a result on the behavior of solutions in more general domains that confirms numerical calculations.
V. Roytburd
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High Field Approximations of the Spherical Harmonics Expansion Model for Semiconductors
, 1998 . We present an asymptotic analysis (with the scaled mean free path as small parameter) of the spherical-harmonics expansion (SHE-) model for semiconductors in the case of a large electric field.
C. Schmeiser +3 more
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Macroscopic Models for Semiconductor Heterostructures
, 1999 The semiconductor Boltzmann equation is considered within a material with a space-dependent band characteristic. Its fluid limit under strong elastic collisions leads to the so-called Spherical Harmonics Expansion (SHE) model.
C. Schmeiser, P. Degond
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AN ELLIPSOIDAL STATISTICAL MODEL FOR GAS MIXTURES
, 2015 International audienceIn this paper, we propose a construction of a new BGK model generalizing the Ellipsoidal Statistical Model ([2], [19]) to the context of gas mixtures.
Brull, Stéphane
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Symplectic Integration of Hamiltonian Wave Equations
, 1994 The numerical integration of a wide class of Hamiltonian partial differential equations by standard symplectic schemes is discussed, with a consistent, Hamiltonian approach.
Robert Mclachlan
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