The problem of stability and blow–up for dissipative evolution equations is treated in this paper by Lyapunov–type methods. The discussion is carried out particularly in the context of evolution operators in a Banach space, with special care given to an appropriate definition of solution, and with the specific examples of degenerate damped wave equations and degenerate parabolic equations as principal applications. Our treatment is expository in intent, based principally on the scientific contributions we gave in six previous papers. In this paper we discuss mainly simplified versions of the results, in order to show the main ideas of the theory and to avoid technicalities.
Existence, stability and blow-up for dissipative evolution equations
PUCCI, Patrizia;
1997
Abstract
The problem of stability and blow–up for dissipative evolution equations is treated in this paper by Lyapunov–type methods. The discussion is carried out particularly in the context of evolution operators in a Banach space, with special care given to an appropriate definition of solution, and with the specific examples of degenerate damped wave equations and degenerate parabolic equations as principal applications. Our treatment is expository in intent, based principally on the scientific contributions we gave in six previous papers. In this paper we discuss mainly simplified versions of the results, in order to show the main ideas of the theory and to avoid technicalities.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
