Qualitative Analysis For Some Quasilinear Parabolic Systems
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| Author | : T. I. Zelenyak |
| Publisher | : Walter de Gruyter |
| Total Pages | : 425 |
| Release | : 2011-09-06 |
| Genre | : Mathematics |
| ISBN | : 311093504X |
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.
| Author | : Franz Rothe |
| Publisher | : Springer |
| Total Pages | : 222 |
| Release | : 2006-12-08 |
| Genre | : Science |
| ISBN | : 3540389172 |
| Author | : Herbert Amann |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 688 |
| Release | : 1995-03-27 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9783764351144 |
This treatise gives an exposition of the functional analytical approach to quasilinear parabolic evolution equations, developed to a large extent by the author during the last 10 years. This approach is based on the theory of linear nonautonomous parabolic evolution equations and on interpolation-extrapolation techniques. It is the only general method that applies to noncoercive quasilinear parabolic systems under nonlinear boundary conditions. The present first volume is devoted to a detailed study of nonautonomous linear parabolic evolution equations in general Banach spaces. It contains a careful exposition of the constant domain case, leading to some improvements of the classical Sobolevskii-Tanabe results. It also includes recent results for equations possessing constant interpolation spaces. In addition, systematic presentations of the theory of maximal regularity in spaces of continuous and Hölder continuous functions, and in Lebesgue spaces, are given. It includes related recent theorems in the field of harmonic analysis in Banach spaces and on operators possessing bounded imaginary powers. Lastly, there is a complete presentation of the technique of interpolation-extrapolation spaces and of evolution equations in those spaces, containing many new results.
| Author | : Shigui Ruan |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 524 |
| Release | : |
| Genre | : Science |
| ISBN | : 9780821871294 |
This book presents the proceedings from the International Conference held in Halifax, NS in July 1997. Funded by The Fields Institute and Le Centre de Recherches Mathématiques, the conference was held in honor of the retirement of Professors Lynn Erbe and Herb I. Freedman (University of Alberta). Featured topics include ordinary, partial, functional, and stochastic differential equations and their applications to biology, epidemiology, neurobiology, physiology and other related areas. The 41 papers included in this volume represent the recent work of leading researchers over a wide range of subjects, including bifurcation theory, chaos, stability theory, boundary value problems, persistence theory, neural networks, disease transmission, population dynamics, pattern formation and more. The text would be suitable for a graduate or advanced undergraduate course study in mathematical biology. Features: An overview of current developments in differential equations and mathematical biology. Authoritative contributions from over 60 leading worldwide researchers. Original, refereed contributions.
| Author | : S.A. Levin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 526 |
| Release | : 2013-03-13 |
| Genre | : Science |
| ISBN | : 3642874223 |
| Author | : T. Nishida |
| Publisher | : Elsevier |
| Total Pages | : 709 |
| Release | : 2011-09-22 |
| Genre | : Mathematics |
| ISBN | : 0080875394 |
Part I of this volume surveys the developments in the analysis of nonlinear phenomena in Japan during the past decade, while Part II consists of up-to-date original papers concerning qualitative theories and their applications.Dealt with here are nonlinear problems related to general analysis, fluid dynamics, mathematical biology and computer sciences, and their underlying mathematical structures, e.g. nonlinear waves and propagations, bifurcation phenomena, chaotic phenomena, and fractals.The volume is dedicated to Professor Masaya Yamaguti in celebration of his 60th birthday.
| Author | : |
| Publisher | : |
| Total Pages | : 576 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Ei Teramoto |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 359 |
| Release | : 2013-03-08 |
| Genre | : Mathematics |
| ISBN | : 3642933602 |
This volume represents the edited proceedings of the International Symposium on Mathematical Biology held in Kyoto, November 10-15, 1985. The symposium was or ganized by an international committee whose members are: E. Teramoto, M. Yamaguti, S. Amari, S.A. Levin, H. Matsuda, A. Okubo, L.M. Ricciardi, R. Rosen, and L.A. Segel. The symposium included technical sessions with a total of 11 invited papers, 49 contributed papers and a poster session where 40 papers were displayed. These Proceedings consist of selected papers from this symposium. This symposium was the second Kyoto meeting on mathematical topics in biology. The first was held in conjunction with the Sixth International Biophysics Congress in 1978. Since then this field of science has grown enormously, and the number of scientists in the field has rapidly increased. This is also the case in Japan. About 80 young japanese scientists and graduate students participated this time. . The sessions were divided into 4 ; , categories: 1) Mathematical Ecology and Population Biology, 2) Mathematical Theory of Developmental Biology and Morphogenesis, 3) Theoretical Neurosciences, and 4) Cell Kinetics and Other Topics. In every session, there were stimulating and active discussions among the participants. We are convinced that the symposium was highly successful in transmitting scientific information across disciplines and in establishing fruitful contacts among the participants. We owe this success to the cooperation of all participants.
| Author | : Michael Z. Zgurovsky |
| Publisher | : Springer |
| Total Pages | : 265 |
| Release | : 2017-07-11 |
| Genre | : Technology & Engineering |
| ISBN | : 3319598406 |
Here, the authors present modern methods of analysis for nonlinear systems which may occur in fields such as physics, chemistry, biology, or economics. They concentrate on the following topics, specific for such systems: (a) constructive existence results and regularity theorems for all weak solutions; (b) convergence results for solutions and their approximations; (c) uniform global behavior of solutions in time; and (d) pointwise behavior of solutions for autonomous problems with possible gaps by the phase variables. The general methodology for the investigation of dissipative dynamical systems with several applications including nonlinear parabolic equations of divergent form, nonlinear stochastic equations of parabolic type, unilateral problems, nonlinear PDEs on Riemannian manifolds with or without boundary, contact problems as well as particular examples is established. As such, the book is addressed to a wide circle of mathematical, mechanical and engineering readers.
| Author | : |
| Publisher | : |
| Total Pages | : 384 |
| Release | : 1982 |
| Genre | : Biological models |
| ISBN | : |
