Stability of the heat and of the wave equations with boundary time-varying delays | Zendy

Serge Nicaise | Zendy; Julie Valein | Zendy; Emilia Fridman | Zendy

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Stability of the heat and of the wave equations with boundary time-varying delays

Author(s) -

Serge Nicaise,

Julie Valein,

Emilia Fridman

Publication year - 2009

Publication title -

discrete and continuous dynamical systems - s

Language(s) - English

Resource type - Journals

eISSN - 1937-1632

pISSN - 1937-1179

DOI - 10.3934/dcdss.2009.2.559

Subject(s) - stability (learning theory) , exponential stability , a priori and a posteriori , mathematics , boundary (topology) , time derivative , heat equation , function (biology) , exponential function , lyapunov function , exponential decay , mathematical analysis , derivative (finance) , boundary value problem , control theory (sociology) , wave equation , exponential growth , physics , computer science , control (management) , philosophy , epistemology , quantum mechanics , nonlinear system , machine learning , evolutionary biology , artificial intelligence , nuclear physics , financial economics , economics , biology

Exponential stability analysis via Lyapunov method is extended to the one-dimensional heat and wave equations with time-varying delay in the boundary conditions. The delay function is admitted to be time-varying with an a priori given upper bound on its derivative, which is less than $1$. Sufficient and explicit conditions are derived that guarantee the exponential stability. Moreover the decay rate can be explicitly computed if the data are given.

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