This book presents in a self-contained form the typical basic properties of solutions to semilinear evolutionary partial differential equations, with special emphasis on global properties. It considers important examples, including the heat, Klein-Gordon, and Schroodinger equations, placing each in the analytical framework which allows the most striking statement of the key properties. With the exceptions of the treatment of the Schroodinger equation, the book employs the most standard methods, each developed in enough generality to cover other cases. This new edition includes a chapter on...
This book presents in a self-contained form the typical basic properties of solutions to semilinear evolutionary partial differential equations, with ...
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 book investigates classical and more recent methods of study for the asymptotic behavior of dissipative continuous dynamical systems with appli...