On the Cauchy problem for nonlinear dissipative systems

The large-time asymptotic behavior of solutions of the Cauchy problem for a system of nonlinear evolutionary equations with dissipation is studied. The approach used in the case of small initial data is based on the construction of solutions by the method of contracting mappings. In the case of large initial data, we will obtain the large-time asymptotics of solutions with a certain symmmetry of a nonlinear term taken into account. In the critical case, it is proved that if the initial data has a nonzero total mass, then the principal term of the large-time asymptotics of a solution is given by the self-similar solution uniquely determined by the total mass of the initial data. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 29, Voronezh Conference-1, 2005.     

T-product of hypoelliptic operators

Asymptotics as t0 for the solution of the Cauchy problem for hypoelliptic equations are obtained. Using these results, the existence of the T-product for hypoelliptic operators is proved as is a theorem on the removal of autonomous brackets in the T-product.Translated from Itogi i Nauki i Tekhniki, Sovremennye Problemy Matematiki, Vol. 8, pp. 137–197, 1977.     

Radiation damping on cryoprobes

Radiation damping on 600 and 800 MHz cryoprobes was investigated. The phase angle β between a vector 90° phase shifted to the precessing magnetization and the rf field induced in the coil was found to depend markedly on whether an FID was being acquired or not. The magnitude of the radiation damping field was sufficiently strong to restore 95% of the equilibrium water magnetization of a 90% H2O sample in a 5 mm sample tube within about 5 ms following a 165° pulse. This can be exploited in water flip-back versions of NOESY and TOCSY experiments of proteins, but care must be taken to limit the effect of the radiation damping field from the water on the Ha protons. Long water-selective pulses can be applied only following corrections. We developed a program for correcting pulse shapes if β is non-zero. The WATERGATE scheme is shown to be insensitive to imperfections introduced by radiation damping.     

On the decay of step for the Korteweg—de Vries—Burgers equation

Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 26, No. 2, pp. 88–93, April–June, 1992.     

Semiclassical Description of Undulator Radiation

Journal of Experimental and Theoretical Physics - We present a semiclassical approximation for treating the radiation from classical currents. In particular, we present exact quantum states of the...     

Control of dynamical systems behavior by parametric perturbations: An analytic approach

The problem of parametric suppression of deterministic chaos is considered. It is proved that certain parametric perturbations of a one-dimensional map with chaotic dynamics can lead to a transition of that map into a regime of regular behavior.     

Asymptotic representation of surface waves in the form of two traveling burgers waves

Chair of General Mathematics, Department of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 29, No. 3, pp. 25–40, July–September, 1995.