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Oscillations of the solutions of nonlinear hyperbolic equations of neutral type.

D.P. Mishev, D.D. Bainov (1992)

Publicacions Matemàtiques

In this paper nonlinear hyperbolic equations of neutral type of a given form are considered, with certain boundary conditions. Under certain constraints on the coefficients of the equation and the boundary conditions, sufficient conditions for oscillation of the solutions of the problems considered are obtained.

Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation

Bao-Zhu Guo, Cheng-Zhong Xu, Hassan Hammouri (2012)

ESAIM: Control, Optimisation and Calculus of Variations

The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper, we are concerned with a particularly interesting case: Boundary output feedback stabilization of a one-dimensional wave equation system for which the...

Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation∗

Bao-Zhu Guo, Cheng-Zhong Xu, Hassan Hammouri (2012)

ESAIM: Control, Optimisation and Calculus of Variations

The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper, we are concerned with a particularly interesting case: Boundary output feedback stabilization of a...

Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation∗

Bao-Zhu Guo, Cheng-Zhong Xu, Hassan Hammouri (2012)

ESAIM: Control, Optimisation and Calculus of Variations

The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper, we are concerned with a particularly interesting case: Boundary output feedback stabilization of a...

Parabolic differential-functional inequalities in viscosity sense

Krzysztof Topolski (1998)

Annales Polonici Mathematici

We consider viscosity solutions for second order differential-functional equations of parabolic type. Initial value and mixed problems are studied. Comparison theorems for subsolutions, supersolutions and solutions are considered.

Propagation of weak discontinuities for quasilinear hyperbolic systems with coefficients functionally dependent on solutions

Małgorzata Zdanowicz, Zbigniew Peradzyński (2013)

Annales Polonici Mathematici

The propagation of weak discontinuities for quasilinear systems with coefficients functionally dependent on the solution is studied. We demonstrate that, similarly to the case of usual quasilinear systems, the transport equation for the intensity of weak discontinuity is quadratic in this intensity. However, the contribution from the (nonlocal) functional dependence appears to be in principle linear in the jump intensity (with some exceptions). For illustration, several examples, including two hyperbolic...

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