Decay estimates of solutions to the IBq equation

Document Type : Research Paper

Authors

School of Mathematics and Statistics‎, ‎North China University of Water Resources and Electric Power‎, ‎Zhengzhou 450011‎, ‎China.

Abstract

‎In this paper we focus on the Cauchy problem for the generalized‎ ‎IBq equation with damped term in $n$-dimensional space‎. ‎We establish the global existence and decay estimates of solution with $L^q(1\leq q\leq 2)$ initial value‎, ‎provided that the initial value is suitably small‎. ‎Moreover‎, ‎we also show that the solution is asymptotic to the solution $u_L$ to the corresponding linear equation as time tends to infinity‎. ‎Finally‎, ‎asymptotic profile of the solution $u_L$ to the linearized problem is also discussed‎.

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References

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Bulletin of the Iranian Mathematical Society
Volume 43, Issue 6
November 2017
Pages 1585-1600

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History

  • Receive Date: 26 November 2015
  • Revise Date: 12 June 2016
  • Accept Date: 16 July 2016

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