1 - 10 of 12 articles
We construct analytically two algebraic closed curves forming aPoincaré–Bendixson annulus for the van der Pol system for all values of its parameter.The inner boundary of the annulus is a closed curve of the zero-level set of a Dulac–Cherkasfunction, which implies that this annulus contains at...
We consider a scenario of transition to chaotic dynamics in a Hamiltonian system ofhomogeneous Yang–Mills fields with three degrees of freedom in the presence of the Higgsmechanism. It is shown that in this system, as in other Hamiltonian and conservative systems ofequations, the key role at the...
For a first-order quasilinear equation with a power-law flux function, generalized entropysolutions of the Cauchy problems are constructed with initial conditions coinciding with a poweror exponential function at minus infinity. In the case of an exponentially growing initial condition,the...
The Lomov regularization method was developed for the Cauchy problem and the mixedproblem for a singularly perturbed parabolic equation in the case of a “simple” rational turningpoint of the limit operator. The maximum principle is used to prove the asymptotic convergenceof the resulting series.
We study a quasihydrodynamic system of equations for a homogeneous (with commonvelocity and temperature) multicomponent gas mixture in the absence of chemical reactions witha common regularizing velocity. For this system, we derive an entropy balance equation withnonnegative entropy production...
For nonlinear evolution equations in a Banach space that depend in twoways—regularly and singularly—on a small parameter, we...
We consider the Riemann–Hilbert problem for a singularly perturbed system of partialdifferential equations of the Cauchy–Riemann type. Using the Lomov regularization method, weobtain sufficient conditions under which the asymptotic solutions of the problem converge in theusual sense.
Using the inverse scattering method, we derive the evolution of the scattering data of anonself-adjoint Sturm–Liouville operator whose potential is a solution of the general loadedKorteweg–de Vries equation with a self-consistent source in the class of rapidly decayingcomplex-valued functions....
Lomov’s regularization method is generalized to nonlinear singularly perturbedintegro-differential equations with rapidly oscillating right-hand side. The influence of the kernelof the integral operator, the nonlinearity, and the rapidly oscillating part on the asymptotics ofthe solution of the...
For a general system of difference (discrete) equations, using the Lyapunov functionmethod, we obtain a number of sufficient conditions for the stability and asymptotic stability ofits solution with respect to part of the variables.
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