کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
844180 | 908578 | 2008 | 13 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Flow invariance for semilinear evolution equations under generalized dissipativity conditions Flow invariance for semilinear evolution equations under generalized dissipativity conditions](/preview/png/844180.png)
Let XX be a real Banach space, let A:D(A)⊂X→XA:D(A)⊂X→X be a linear operator which is the infinitesimal generator of a (C0)(C0)-semigroup and let B:D⊂X→XB:D⊂X→X be a nonlinear perturbation which is continuous on level sets of DD with respect to a lower semicontinuous (l.s.c.) functional φφ. We discuss the existence of a nonlinear semigroup SS providing mild solutions to the semilinear abstract Cauchy problem (SP;x)u′(t)=(A+B)u(t),t>0;u(0)=x∈D and satisfying a certain Lipschitz-like estimation and an exponential growth condition. Using the discrete schemes approximation, it is proved that the combination of a subtangential condition and a semilinear stability condition in terms of a metric-like functional is necessary and sufficient for the generation of such a semigroup SS.
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 68, Issue 2, 15 January 2008, Pages 443–455