Global attracting set, exponential decay and stability in distribution of neutral SPDEs driven by additive $\alpha$-stable processes

Kai  Liu; Zhi  Li

doi:10.3934/dcdsb.2016110

Article Contents

2016, Volume 21, Issue 10: 3551-3573. Doi: 10.3934/dcdsb.2016110

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Global attracting set, exponential decay and stability in distribution of neutral SPDEs driven by additive $\alpha$-stable processes

Kai Liu^1, and
Zhi Li^2,

1.
School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387
2.
School of Information and Mathematics, Yangtze University, Jingzhou 434023

Received: January 2016

Revised: June 2016

Published: December 2016

Abstract / Introduction Related Papers Cited by

Abstract

In this paper, we are concerned with a class of neutral stochastic partial differential equations driven by $\alpha$-stable processes. By combining some stochastic analysis techniques, tools from semigroup theory and delay integral inequalities, we identify the global attracting sets of the equations under investigation. Some sufficient conditions ensuring the exponential decay of mild solutions in the $p$-th moment to the stochastic systems are obtained. Subsequently, by employing a weak convergence approach, we try to establish some stability conditions in distribution of the segment processes of mild solutions to the stochastic systems under consideration. Last, an example is presented to illustrate our theory in the work.

Keywords:

Mathematics Subject Classification: 60H15, 60G15, 39B05.

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