arXiv:1709.07737 Abstract | arXiv Analytics

arXiv:1709.07737 [math.AP]Abstract References Reviews Resources

Global Stability for a Class of Nonlinear PDE with non-local term

Published 2017-09-22Version 1

This paper is concerned with establishing global asymptotic stability results for a class of non-linear PDE which have some similarity to the PDE of the Lifschitz-Slyozov-Wagner model. 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 maximal properties. These are established by using the methods of optimal control theory.

Comments: 49 pages

Categories: math.AP

Subjects: 35F20, 34K20, 49L20

Keywords: global stability, nonlinear pde, non-local term, establishing global asymptotic stability results, differential delay equation

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