Qualitative Analysis for Some Quasilinear Parabolic Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Qualitative Analysis for Some Quasilinear Parabolic Systems write by P. de Mottoni. This book was released on 1979. Qualitative Analysis for Some Quasilinear Parabolic Systems available in PDF, EPUB and Kindle.
Linear and Quasilinear Parabolic Systems: Sobolev Space Theory
Linear and Quasilinear Parabolic Systems: Sobolev Space Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Linear and Quasilinear Parabolic Systems: Sobolev Space Theory write by David Hoff. This book was released on 2020-11-18. Linear and Quasilinear Parabolic Systems: Sobolev Space Theory available in PDF, EPUB and Kindle. 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.
Qualitative Theory of Parabolic Equations, Part 1
Qualitative Theory of Parabolic Equations, Part 1 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Qualitative Theory of Parabolic Equations, Part 1 write by T. I. Zelenyak. This book was released on 2011-09-06. Qualitative Theory of Parabolic Equations, Part 1 available in PDF, EPUB and Kindle. 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.
Linear and Quasilinear Parabolic Problems
Linear and Quasilinear Parabolic Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Linear and Quasilinear Parabolic Problems write by Herbert Amann. This book was released on 1995-03-27. Linear and Quasilinear Parabolic Problems available in PDF, EPUB and Kindle. 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.
Regularity of Solutions for Some Quasilinear Parabolic Systems
Regularity of Solutions for Some Quasilinear Parabolic Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Regularity of Solutions for Some Quasilinear Parabolic Systems write by A. Koshelev. This book was released on 1991. Regularity of Solutions for Some Quasilinear Parabolic Systems available in PDF, EPUB and Kindle.
