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A note on critical times of 2 × 2 quasilinear hyperbolic systems

Ivan Straškraba — 1984

Aplikace matematiky

In this paper the exact formula for the critical time of generating discontinuity (shock wave) in a solution of a 2 × 2 quasilinear hyperbolic system is derived. The applicability of the formula in the engineering praxis is shown on one-dimensional equations of isentropic non-viscous compressible fluid flow.

Solution of a linear model of a single-piston pump by means of methods for differential equations in Hilbert spaces

Ivan Straškraba — 1986

Aplikace matematiky

A mathematical model of a fluid flow in a single-piston pump is formulated and solved. Variation of pressure and rate of flow in suction and delivery piping respectively is described by linearized Euler equations for barotropic fluid. A new phenomenon is introduced by a boundary condition with discontinuous coefficient describing function of a valve. The system of Euler equations is converted to a second order equation in the space L 2 ( 0 , l ) where l is length of the pipe. The existence, unicity and stability...

Two phase flow arising in hydraulics

Ivan Straškraba — 2015

Applications of Mathematics

The aim of this paper is to proceed in the study of the system which will be specified below. The system concerns fluid flow in a simple hydraulic system consisting of a pipe with generator on one side and a valve or some more complicated hydraulic elements on the other end of the pipe. The purpose of the research is a rigorous mathematical analysis of the corresponding linearized system. Here, we analyze the linearized problem near the fixed steady state which already have been explicitly described....

Stabilization of solutions to a differential-delay equation in a Banach space

J. J. KolihaIvan Straškraba — 1997

Annales Polonici Mathematici

A parameter dependent nonlinear differential-delay equation in a Banach space is investigated. It is shown that if at the critical value of the parameter the problem satisfies a condition of linearized stability then the problem exhibits a stability which is uniform with respect to the whole range of the parameter values. The general theorem is applied to a diffusion system with applications in biology.

Power bounded and exponentially bounded matrices

Jaromír J. KolihaIvan Straškraba — 1999

Applications of Mathematics

The paper gives a new characterization of eigenprojections, which is then used to obtain a spectral decomposition for the power bounded and exponentially bounded matrices. The applications include series and integral representations of the Drazin inverse, and investigation of the asymptotic behaviour of the solutions of singular and singularly perturbed differential equations. An example is given of localized travelling waves for a system of conservation laws.

Stability in nonlinear evolution problems by means of fixed point theorems

Jaromír J. KolihaIvan Straškraba — 1997

Commentationes Mathematicae Universitatis Carolinae

The stabilization of solutions to an abstract differential equation is investigated. The initial value problem is considered in the form of an integral equation. The equation is solved by means of the Banach contraction mapping theorem or the Schauder fixed point theorem in the space of functions decreasing to zero at an appropriate rate. Stable manifolds for singular perturbation problems are compared with each other. A possible application is illustrated on an initial-boundary-value problem for...

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