The exponential stability of neutral stochastic delay partial differential equations

By Tomás Caraballo, José Real, Takeshi Taniguchi. 2007

82 citations recorded by the source corpus.

In this paper we analyze the almost sure exponential stability and ultimate boundedness of the solutions to a class of neutral stochastic semilinear partial delay differential equations. These kind of equations arise in problems related to coupled oscillators in a noisy environment, or in viscoeslastic materials under random or stochastic influences.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/817bd2313def15130e221a6bb66c6a66ebf9a85f

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In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Exponential stability for stochastic neutral partial functional differential equations (2009, methodology): “5) (H3) The mapping f (t, x) satisfies that there exists a number α ∈ [0,1] such that for any x, y ∈ Cr and t 0, f (t, x) ∈ D((−A)α) and ∣∣(−A)α f (t, x)− (−A)α f (t, y)∣∣ C4‖x− y‖Cr , C4 > 0.”
Non--autonomous and random attractors for delay random semilinear equations without uniqueness (2008, background): “[14], [7], [6], [15], [26]) or others with non-uniqueness of solutions or modelled by differential inclusions (Caraballo et al.”
Fixed Points and Stability of Stochastic Neutral Partial Differential Equations with Infinite Delays (2009, background): “[3] discussed the existence and uniqueness, almost sure exponential stability and ultimate boundedness of the solutions to a class of neutral stochastic semilinear partial delay differential equations.”