Blow-up for Joseph–Egri equation: Theoretical approach and numerical analysis

This work develops the theory of the blow-up phenomena for Joseph–Egri equation. The existence of the nonextendable solution of two initial-boundary value problems (on a segment and a half-line) is demonstrated. Sufficient conditions of the finite-time blow-up of these solutions, as well as the analytical estimates of the blow-up time, are obtained. A numerical method that allows to precise the blow-up moment for specified initial data is proposed. © 2020 John Wiley & Sons, Ltd

Local solvability and a priori estimates for classical solutions to an equation of Benjamin-Bona-Mahony-Bürgers type

We establish the local (in time) solvability in the classical sense for the Cauchy problem and first and second boundary-value problems on the half-line for a nonlinear equation similar to Benjamin-Bona-Mahony-Bürgers-type equation. We also derive an a priori estimate that implies sufficient blow-up conditions for the second boundary-value problem. We obtain analytically an upper bound of the blow-up time and refine it numerically using Richardson effective accuracy order technique. © 2020 John Wiley & Sons, Ltd

On the blow-up phenomena for a 1-dimensional equation of ion sound waves in a plasma: Analytical and numerical investigation

The initial-boundary value problem for an equation of ion sound waves in plasma is considered. A theorem on nonextendable solution is proved. The blow-up phenomena are studied. The sufficient blow-up conditions and the blow-up time are analysed by the method of the test functions. This analytical a priori information is used in the numerical experiments, which are able to determine the process of the solution's blow-up more accurately. Copyright © 2018 John Wiley & Sons, Ltd

Blow-up of solutions of a full non-linear equation of ion-sound waves in a plasma with non-coercive non-linearities

We consider a series of initial- boundary value problems for the equation of ion- sound waves in a plasma. For each of them we prove the local (in time) solubility and perform an analytical- numerical study of the blow-up of solutions. We use the method of test functions to obtain sufficient conditions for finite-time blow-up and an upper bound for the blow-up time. In concrete numerical examples we improve these bounds numerically using the mesh refinement method. Thus the analytical and numerical parts of the investigation complement each other. The time interval for the numerical modelling is chosen in accordance with the analytically obtained upper bound for the blow-up time. In return, numerical calculations specify the moment and pattern of this blow-up. © 2018 RAS(DoM) and LMS

On the blow-up phenomena for a 1-dimensional equation of ion sound waves in a plasma: Analytical and numerical investigation

The initial-boundary value problem for an equation of ion sound waves in plasma is considered. A theorem on nonextendable solution is proved. The blow-up phenomena are studied. The sufficient blow-up conditions and the blow-up time are analysed by the method of the test functions. This analytical a priori information is used in the numerical experiments, which are able to determine the process of the solution's blow-up more accurately. Copyright © 2018 John Wiley & Sons, Ltd

Blow-up of solutions of a full non-linear equation of ion-sound waves in a plasma with non-coercive non-linearities

We consider a series of initial- boundary value problems for the equation of ion- sound waves in a plasma. For each of them we prove the local (in time) solubility and perform an analytical- numerical study of the blow-up of solutions. We use the method of test functions to obtain sufficient conditions for finite-time blow-up and an upper bound for the blow-up time. In concrete numerical examples we improve these bounds numerically using the mesh refinement method. Thus the analytical and numerical parts of the investigation complement each other. The time interval for the numerical modelling is chosen in accordance with the analytically obtained upper bound for the blow-up time. In return, numerical calculations specify the moment and pattern of this blow-up. © 2018 RAS(DoM) and LMS

Разработка установки для эндоскопических операций на экспериментальных животных

Grebenyuk, A.I., Chizh, N.A., Byzov, D.V., Rohoza, L.A., Antonenko, E.A., Lukyanenko, P.G., Sandomirsky, B.P. (2016). Designing of Device for Endoscopic Surgery In Experimental Animals. Problems of Cryobiology and Cryomedicine, 26(2), 189. https://doi.org/10.15407/cryo26.02.189Designing of Device for Endoscopic Surgery In Experimental Animal