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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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The Convergence Problem for Dissipative Autonomous Systems - Classical Methods and Recent Advances (Paperback, 1st ed. 2015)
Loot Price: R1,190
Discovery Miles 11 900
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The Convergence Problem for Dissipative Autonomous Systems - Classical Methods and Recent Advances (Paperback, 1st ed. 2015)
Series: SpringerBriefs in Mathematics
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The book investigates classical and more recent methods of study
for the asymptotic behavior of dissipative continuous dynamical
systems with applications to ordinary and partial differential
equations, the main question being convergence (or not) of the
solutions to an equilibrium. After reviewing the basic concepts of
topological dynamics and the definition of gradient-like systems on
a metric space, the authors present a comprehensive exposition of
stability theory relying on the so-called linearization method. For
the convergence problem itself, when the set of equilibria is
infinite, the only general results that do not require very special
features of the non-linearities are presently consequences of a
gradient inequality discovered by S. Lojasiewicz. The application
of this inequality jointly with the so-called Liapunov-Schmidt
reduction requires a rigorous exposition of Semi-Fredholm operator
theory and the theory of real analytic maps on infinite dimensional
Banach spaces, which cannot be found anywhere in a readily
applicable form. The applications covered in this short text are
the simplest, but more complicated cases are mentioned in the final
chapter, together with references to the corresponding specialized
papers.
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