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Second and third order perturbation solutions of a generalized Burgers' equation
Acta Mechanica, 1986The differential equation \(u_{\tau}-uu_ x=k(u_{xx}+cu_{x\tau})\) with initial values on \(\tau =0\) is considered. When \(c\neq 0\) this represents a hyperbolic generalization of Burgers' equation. For \(k\ll 1\) perturbation solutions are obtained, the outer solution being given completely up to third order, the inner solution (i.e.
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Differential Equations, 2023
A second-order ordinary differential equation with a three-position hysteresis relay characteristic and a periodic perturbation function is considered. The existence theorem is proved for an oscillatory solution with a complete traversal of the characteristic with a possible exit into its saturation zones in some finite time and with a closed phase ...
Yevstafyeva, V. V. +2 more
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A second-order ordinary differential equation with a three-position hysteresis relay characteristic and a periodic perturbation function is considered. The existence theorem is proved for an oscillatory solution with a complete traversal of the characteristic with a possible exit into its saturation zones in some finite time and with a closed phase ...
Yevstafyeva, V. V. +2 more
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Journal of Elasticity, 1997
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DELL'ISOLA, Francesco +2 more
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DELL'ISOLA, Francesco +2 more
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Perturbations of solutions of the sinorini problem for a second-order scalar equation
Mathematical Notes of the Academy of Sciences of the USSR, 1990See the review in Zbl 0699.35012.
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Journal of Quantitative Spectroscopy and Radiative Transfer, 1995
A second order perturbation expansion solution is obtained for solar radiative transfer in a medium with a horizontally arbitrary periodic variation of extinction coefficient. The calculations show that the perturbation solution series is convergent. The cloud albedo changes from the unperturbed value when the second order perturbation correction is ...
J. Li, D.J.W. Geldart, Petr Chýlek
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A second order perturbation expansion solution is obtained for solar radiative transfer in a medium with a horizontally arbitrary periodic variation of extinction coefficient. The calculations show that the perturbation solution series is convergent. The cloud albedo changes from the unperturbed value when the second order perturbation correction is ...
J. Li, D.J.W. Geldart, Petr Chýlek
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Zeitschrift f�r angewandte Mathematik und Physik, 2005
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El-Gamel, Mohamed, Cannon, John R.
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El-Gamel, Mohamed, Cannon, John R.
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Journal of the Franklin Institute, 1986
The paper is the continuation of two previous ones, concerning the same subject and by the same author [ibid. 316, 273-277 (1983; Zbl 0529.39002) and ibid. 320, 169-174 (1985; Zbl 0589.39004)]. Here the purpose is to construct first and second approximations to the solutions of the following class of nonlinear difference equations \[ x_{k+1}-(2 \cos ...
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The paper is the continuation of two previous ones, concerning the same subject and by the same author [ibid. 316, 273-277 (1983; Zbl 0529.39002) and ibid. 320, 169-174 (1985; Zbl 0589.39004)]. Here the purpose is to construct first and second approximations to the solutions of the following class of nonlinear difference equations \[ x_{k+1}-(2 \cos ...
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Banach Center Publications, 2014
In this work we will consider a class of second order perturbed Hamiltonian systems with a superquadratic growth condition on a time periodic potential and a small aperiodic forcing term. To get an almost homoclinic solution we approximate the original system by time periodic ones with larger and larger time periods.
Marek Izydorek, Joanna Janczewska
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In this work we will consider a class of second order perturbed Hamiltonian systems with a superquadratic growth condition on a time periodic potential and a small aperiodic forcing term. To get an almost homoclinic solution we approximate the original system by time periodic ones with larger and larger time periods.
Marek Izydorek, Joanna Janczewska
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Journal of Mathematical Sciences, 2020
Sufficient conditions for the asymptotic stability of the solutions of a second-order linear integro-differential equation of the Volterra type are established in the case where the solutions of the corresponding second-order linear differential equation may have no property under study.
Iskandarov, Samandar +1 more
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Sufficient conditions for the asymptotic stability of the solutions of a second-order linear integro-differential equation of the Volterra type are established in the case where the solutions of the corresponding second-order linear differential equation may have no property under study.
Iskandarov, Samandar +1 more
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Applied Mathematics and Mechanics, 1988
In this note a boundary value problem for a second order singularly perturbed differential-difference equation is considered. The asymptotic expansions of the formal solution in six boundary layer regions are constructed using the method of two-variables expansion.
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In this note a boundary value problem for a second order singularly perturbed differential-difference equation is considered. The asymptotic expansions of the formal solution in six boundary layer regions are constructed using the method of two-variables expansion.
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