Lp-Lqestimates for a class of pseudo-differential equations and their applications
β Scribed by Qing Quan Deng; Xiao Hua Yao
- Publisher
- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2011
- Tongue
- English
- Weight
- 266 KB
- Volume
- 27
- Category
- Article
- ISSN
- 1439-7617
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We study a class of nonlinear evolutionary equations generated by a pseudo-differential operator with the elliptic principal symbol and with nonlinearities of the form G(u x ) where cΞ· 2 β€ G(Ξ·) β€ CΞ· 2 for large |Ξ·|. We demonstrate existence of a universal absorbing set, and a compact attractor, and
The problem of Lyapunov stability for functional differential equations in Hilbert spaces is studied. The system to be considered is non-autonomous and the delay is timevarying. Known results on this problem are based on the Gronwall inequality yielding relative conservative bounds on nonlinear pert