Qualitative Theory of Parabolic Equations, Part 1
Qualitative Theory of Parabolic Equations, Part 1

Author: T. I. Zelenyak

Publisher: Walter de Gruyter

Published: 2011-09-06

Total Pages: 425

ISBN-13: 311093504X

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In the qualitative theory of ordinary differential equations, the Liapunov method plays a fundamental role. To use their analogs for the analysis of stability of solutions to parabolic, hyperparabolic, and other nonclassical equations and systems, time-invariant a priori estimates have to be devised for solutions. In this publication only parabolic problems are considered. Here lie, mainly, the problems which have been investigated most thoroughly --- the construction of Liapunov functionals which naturally generalize Liapunov functions for nonlinear parabolic equations of the second order with one spatial variable. The authors establish stabilizing solutions theorems, and the necessary and sufficient conditions of general and asymptotic stability of stationary solutions, including the so-called critical case. Attraction domains for stable solutions of mixed problems for these equations are described. Furthermore, estimates for the number of stationary solutions are obtained.

Handbook of Differential Equations: Ordinary Differential Equations
Handbook of Differential Equations: Ordinary Differential Equations

Author: A. Canada

Publisher: Elsevier

Published: 2006-08-21

Total Pages: 753

ISBN-13: 0080463819

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This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience. These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for reseach, learing and teaching. This volumes consists of seven chapters covering a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume. - Covers a variety of problems in ordinary differential equations - Pure mathematical and real world applications - Written for mathematicians and scientists of many related fields

Fokker–Planck–Kolmogorov Equations
Fokker–Planck–Kolmogorov Equations

Author: Vladimir I. Bogachev

Publisher: American Mathematical Society

Published: 2022-02-10

Total Pages: 495

ISBN-13: 1470470098

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This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker–Planck–Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.

New Directions and Applications in Control Theory
New Directions and Applications in Control Theory

Author: Wijesuriya P. Dayawansa

Publisher: Springer Science & Business Media

Published: 2005-08-31

Total Pages: 420

ISBN-13: 9783540239536

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This volume contains a collection of papers in control theory and applications presented at a conference in honor of Clyde Martin on the occasion of his 60th birthday, held in Lubbock, Texas, November 14-15, 2003.

A Practical Guide to Geometric Regulation for Distributed Parameter Systems
A Practical Guide to Geometric Regulation for Distributed Parameter Systems

Author: Eugenio Aulisa

Publisher: CRC Press

Published: 2015-06-18

Total Pages: 292

ISBN-13: 1482240149

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A Practical Guide to Geometric Regulation for Distributed Parameter Systems provides an introduction to geometric control design methodologies for asymptotic tracking and disturbance rejection of infinite-dimensional systems. The book also introduces several new control algorithms inspired by geometric invariance and asymptotic attraction for a wid

Analytical and Numerical Methods for Convection-dominated and Singularly Perturbed Problems
Analytical and Numerical Methods for Convection-dominated and Singularly Perturbed Problems

Author: Lubin Vulkov

Publisher: Nova Publishers

Published: 2000

Total Pages: 298

ISBN-13: 9781560728481

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This volume is the Proceedings of the Workshop on Analytical and Computational Methods for Convection-Dominated and Singularly Perturbed Problems, which took place in Lozenetz, Bulgaria, 27-31 August 1998. The workshop attracted about 50 participants from 12 countries. The volume includes 13 invited lectures and 19 contributed papers presented at the workshop and thus gives an overview of the latest developments in both the theory and applications of advanced numerical methods to problems having boundary and interior layers. There was an emphasis on experiences from the numerical analysis of such problems and on theoretical developments. The aim of the workshop was to provide an opportunity for scientists from the East and the West, who develop robust methods for singularly perturbed and related problems and also who apply these methods to real-life problems, to discuss recent achievements in this area and to exchange ideas with a view of possible research co-operation.

Parabolic Equations in Biology
Parabolic Equations in Biology

Author: Benoît Perthame

Publisher: Springer

Published: 2015-09-09

Total Pages: 204

ISBN-13: 331919500X

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This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.

Stability of Motion of Nonautonomous Systems (Methods of Limiting Equations)
Stability of Motion of Nonautonomous Systems (Methods of Limiting Equations)

Author: Junji Kato

Publisher: Routledge

Published: 2019-09-09

Total Pages: 280

ISBN-13: 1351414852

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Continuing the strong tradition of functional analysis and stability theory for differential and integral equations already established by the previous volumes in this series, this innovative monograph considers in detail the method of limiting equations constructed in terms of the Bebutov-Miller-Sell concept, the method of comparison, and Lyapunov's direct method based on scalar, vector and matrix functions. The stability of abstract compacted and uniform dynamic processes, dispersed systems and evolutionary equations in Banach space are also discussed. For the first time, the method first employed by Krylov and Bogolubov in their investigations of oscillations in almost linear systems is applied to a new field: that of the stability problem of systems with small parameters. This important development should facilitate the solution of engineering problems in such areas as orbiting satellites, rocket motion, high-speed vehicles, power grids, and nuclear reactors.

Mathematics And Mathematics Education, Procs Of The Third Intl Palestinian Conf
Mathematics And Mathematics Education, Procs Of The Third Intl Palestinian Conf

Author: Raghib Abu-saris

Publisher: World Scientific

Published: 2002-05-24

Total Pages: 358

ISBN-13: 9814490342

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This volume covers a wide range of areas in mathematics and mathematics education. There is emphasis on applied mathematics, including partial differential equations, dynamical systems, and difference equations. Other areas represented include algebra and number theory, statistics, and issues in mathematics education.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)