The problem of asymptotic stability for second order ordinary differential equations is well–known in the literature. Recently, various extensions of this work have been given for the case of second order hyperbolic systems. On the other hand, the situation for parabolic systems has received much less discussion, so that a study of this problem seems worthwhile. In this paper we develop an asymptotic stability theory for nonlinear parabolic systems, adapting in a nontrivial way the analogous results on asymptotic stability we established for nonautonomous dessipative wave systems in [Comm. Pure Appl. Math. 49 (1996), 177-216]. A number of important special cases and extensions of the main theorem are also considered.
Asymptotic stability for nonlinear parabolic systems
PUCCI, Patrizia;
1996
Abstract
The problem of asymptotic stability for second order ordinary differential equations is well–known in the literature. Recently, various extensions of this work have been given for the case of second order hyperbolic systems. On the other hand, the situation for parabolic systems has received much less discussion, so that a study of this problem seems worthwhile. In this paper we develop an asymptotic stability theory for nonlinear parabolic systems, adapting in a nontrivial way the analogous results on asymptotic stability we established for nonautonomous dessipative wave systems in [Comm. Pure Appl. Math. 49 (1996), 177-216]. A number of important special cases and extensions of the main theorem are also considered.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.