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Author : P. de Mottoni
Release : 1979
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Qualitative Analysis for Some Quasilinear Parabolic Systems by : P. de Mottoni
Download or read book Qualitative Analysis for Some Quasilinear Parabolic Systems written by P. de Mottoni. This book was released on 1979. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David Hoff
Release : 2020-11-18
Genre : Education
Kind : eBook
Book Rating : 617/5 ( reviews)
Book Synopsis Linear and Quasilinear Parabolic Systems: Sobolev Space Theory by : David Hoff
Download or read book Linear and Quasilinear Parabolic Systems: Sobolev Space Theory written by David Hoff. This book was released on 2020-11-18. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a systematic theory of weak solutions in Hilbert-Sobolev spaces of initial-boundary value problems for parabolic systems of partial differential equations with general essential and natural boundary conditions and minimal hypotheses on coefficients. Applications to quasilinear systems are given, including local existence for large data, global existence near an attractor, the Leray and Hopf theorems for the Navier-Stokes equations and results concerning invariant regions. Supplementary material is provided, including a self-contained treatment of the calculus of Sobolev functions on the boundaries of Lipschitz domains and a thorough discussion of measurability considerations for elements of Bochner-Sobolev spaces. This book will be particularly useful both for researchers requiring accessible and broadly applicable formulations of standard results as well as for students preparing for research in applied analysis. Readers should be familiar with the basic facts of measure theory and functional analysis, including weak derivatives and Sobolev spaces. Prior work in partial differential equations is helpful but not required.
Author : T. I. Zelenyak
Release : 2011-09-06
Genre : Mathematics
Kind : eBook
Book Rating : 04X/5 ( reviews)
Book Synopsis Qualitative Theory of Parabolic Equations, Part 1 by : T. I. Zelenyak
Download or read book Qualitative Theory of Parabolic Equations, Part 1 written by T. I. Zelenyak. This book was released on 2011-09-06. Available in PDF, EPUB and Kindle. Book excerpt: 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 : A. Koshelev
Release : 1991
Genre :
Kind : eBook
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Book Synopsis Regularity of Solutions for Some Quasilinear Parabolic Systems by : A. Koshelev
Download or read book Regularity of Solutions for Some Quasilinear Parabolic Systems written by A. Koshelev. This book was released on 1991. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Franz Rothe
Release : 2006-12-08
Genre : Science
Kind : eBook
Book Rating : 172/5 ( reviews)
Book Synopsis Global Solutions of Reaction-Diffusion Systems by : Franz Rothe
Download or read book Global Solutions of Reaction-Diffusion Systems written by Franz Rothe. This book was released on 2006-12-08. Available in PDF, EPUB and Kindle. Book excerpt:
