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Global Stability for a Class of Nonlinear PDE with Non-local Term

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Abstract

This paper is concerned with establishing global asymptotic stability results for a class of non-linear PDE, in which the nonlinearity enters as a scalar multiple which is non-local. The method of proof does not involve a Lyapounov function. It is shown that stability for the PDE is equivalent to stability for a differential delay equation. Stability for the delay equation is proven by exploiting certain monotonicity properties. These are established by using the methods of optimal control theory.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109-1109, USA

    Joseph G. Conlon

  2. Department of Mathematics and Statistics, University of Michigan-Dearborn, Dearborn, MI, 48128, USA

    Michael Dabkowski

Authors
  1. Joseph G. Conlon
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  2. Michael Dabkowski
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Correspondence to Joseph G. Conlon.

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Communicated by Eric A. Carlen.

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Conlon, J.G., Dabkowski, M. Global Stability for a Class of Nonlinear PDE with Non-local Term. J Stat Phys 178, 420–471 (2020). https://doi.org/10.1007/s10955-019-02437-7

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  • DOI: https://doi.org/10.1007/s10955-019-02437-7

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