Author : T. I. Zelenyak
Release : 2011-09-06
Genre : Mathematics
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Book Rating : 04X/5 ( reviews)

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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.