On some singular hyperbolic evolution equations in Hilbert spaces

1986 ◽  
pp. 208-215
Author(s):  
M. Povoas
Keyword(s):  
Hilbert Spaces ◽  
Evolution Equations

scholarly journals Domain invariance for local solutions of semilinear evolution equations in Hilbert spaces

2020 ◽  
Vol 102 (1) ◽  
pp. 287-318
Author(s):  
Piermarco Cannarsa ◽  
Giuseppe Da Prato ◽  
Hélène Frankowska
Keyword(s):  
Hilbert Spaces ◽  
Evolution Equations ◽  
Local Solutions ◽  
Semilinear Evolution Equations

scholarly journals Almost Automorphic Solutions to Nonautonomous Stochastic Functional Integrodifferential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Li Xi-liang ◽  
Han Yu-liang
Keyword(s):  
Hilbert Spaces ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Stochastic Equations ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Almost Automorphic ◽  
Banach Contraction ◽  
Stability Results ◽  
Stochastic Functional

This paper concerns the square-mean almost automorphic solutions to a class of abstract semilinear nonautonomous functional integrodifferential stochastic evolution equations in real separable Hilbert spaces. Using the so-called “Acquistapace-Terreni” conditions and Banach contraction principle, the existence, uniqueness, and asymptotical stability results of square-mean almost automorphic mild solutions to such stochastic equations are established. As an application, square-mean almost automorphic solution to a concrete nonautonomous integro-differential stochastic evolution equation is analyzed to illustrate our abstract results.

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