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8 results on '"damped equations"'

3. Nonlocal quasilinear damped differential inclusions

Author

Mouffak Benchohra, Efrosini P. Gatsori, and Sotiris K. Ntouyas

Subjects
Initial value problems, multivalued map, damped equations, mild solution, evolution inclusion, nonlocal condition, fixed point., Mathematics, QA1-939
Abstract

In this paper we investigate the existence of mild solutions to second order initial value problems for a class of damped differential inclusions with nonlocal conditions. By using suitable fixed point theorems, we study the case when the multivalued map has convex and nonconvex values.

Published
2002

4. Some oscillation criteria for a class of second order nonlinear damped differential equations.

Author

Salhin, Ambarka Abdalla, Din, Ummul Khair Salma, Ahmad, Rokiah Rozita, and Md Noorani, Mohd Salmi

Subjects
*NONLINEAR differential equations, *OSCILLATIONS, *RICCATI equation, *AVERAGING method (Differential equations), *NONLINEAR theories
Abstract

A class of second order nonlinear damped differential equations is studied and several new oscillation conditions are obtained. Our results extend, improve and unify a number of existing results and handle the cases which are not covered by known criteria. [ABSTRACT FROM AUTHOR]

Published
2014
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5. A generalized interpolation inequality and its application to the stabilization of damped equations

Author

Bégout, Pascal and Soria, Fernando

Subjects
*NUMERICAL analysis, *VIBRATION (Mechanics), *WAVES (Physics), *DIFFERENTIAL equations
Abstract

Abstract: In this paper, we establish a generalized Hölder''s or interpolation inequality for weighted spaces in which the weights are non-necessarily homogeneous. We apply it to the stabilization of some damped wave-like evolution equations. This allows obtaining explicit decay rates for smooth solutions for more general classes of damping operators. In particular, for models, we can give an explicit decay estimate for pointwise damping mechanisms supported on any strategic point. [Copyright &y& Elsevier]

Published
2007
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6. A Generalized Interpolation Inequality and its Application to the Stabilization of Damped Equations

Author

Fernando Soria, Pascal Bégout, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse et Probabilités (LAE), Université d'Évry-Val-d'Essonne (UEVE), Departamento de Matematicas (UAM), Universidad Autónoma de Madrid (UAM)-Universidad Autónoma de Madrid (UAM), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse et Probabilités, Université d'Évry-Val-d'Essonne (UEVE)-PRES Universud Paris-Fédération de Mathématiques d'Evry Val d'Essonne, and Universidad Autonoma de Madrid (UAM)-Universidad Autonoma de Madrid (UAM)

Subjects
0209 industrial biotechnology, damped equations, 02 engineering and technology, 01 natural sciences, Mathematics - Analysis of PDEs, 020901 industrial engineering & automation, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Point (geometry), 0101 mathematics, [MATH]Mathematics [math], B- ECONOMIE ET FINANCE, Mathematics, Pointwise, damping control, Applied Mathematics, 010102 general mathematics, Mathematical analysis, interpolation inequality, G- MATHEMATIQUES, Interpolation inequality, stabilization, Homogeneous, generalized Hölder's inequality, 2000 Mathematics Subject Classification: 93D15 (35B37, 35L70, 93B52, 93C20), Analysis, Analysis of PDEs (math.AP)
Abstract

International audience; In this paper, we establish a generalized Hölder's or interpolation inequality for weighted spaces in which the weights are non-necessarily homogeneous. We apply it to the stabilization of some damped wave-like evolution equations. This allows obtaining explicit decay rates for smooth solutions for more general classes of damping operators. In particular, for $1-d$ models, we can give an explicit decay estimate for pointwise damping mechanisms supported on any strategic point.

Published
2007
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8. Asymptotic Bounds for Solutions to a System of Damped Integrodifferential Equations of Electromagnetic Theory.

Author

SOUTH CAROLINA UNIV COLUMBIA DEPT OF MATHEMATICS COMPUTER SCIENCE AND STATISTICS, Bloom,Frederick, SOUTH CAROLINA UNIV COLUMBIA DEPT OF MATHEMATICS COMPUTER SCIENCE AND STATISTICS, and Bloom,Frederick

Abstract

For the system of damped integrodifferential equations which govern the evolution of the electric induction field in a class of rigid holohedral isotropic dielectrics of the type introduced by Toupin and Rivlin, conditions on the memory functions are deduced which imply that the L2 norms of such induction fields are bounded away from zero even as the damping grows in an unbounded manner; explicit lower bounds for the L2 norms of the induction fields in such dielectrics are derived as t increases without limit. (Author)

Published
1979

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