Large deviations for stochastic tidal dynamics equation

Suvinthra, Murugan; Sritharan, S. S.; Balachandran, K.

doi:10.31390/cosa.9.4.04

Cited by 8 publications

(12 citation statements)

References 33 publications

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“…Our proof is based on Theorem 4.4 of Brzeźniak et al [9] and Theorem 3.2 of Suvinthra et al [47]. Let us consider the function ψ(t) ∈ H 1 (−δ, T + δ) with ψ(0) = 1.…”

Section: Energy Estimates and Existence Resultsmentioning

confidence: 97%

Stochastic Control of Tidal Dynamics Equation with Lévy Noise

2017

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In this work we first present the existence, uniqueness and regularity of the strong solution of the tidal dynamics model perturbed by Lévy noise. Monotonicity arguments have been exploited in the proofs. We then formulate a martingale problem of Stroock and Varadhan associated to an initial value control problem and establish existence of optimal controls. 2010 Mathematics Subject Classification. 35Q35, 60H15, 76D03, 76D55.

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“…Our proof is based on Theorem 4.4 of Brzeźniak et al [9] and Theorem 3.2 of Suvinthra et al [47]. Let us consider the function ψ(t) ∈ H 1 (−δ, T + δ) with ψ(0) = 1.…”

Section: Energy Estimates and Existence Resultsmentioning

confidence: 97%

Stochastic Control of Tidal Dynamics Equation with Lévy Noise

2017

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“…Since H −1 (Ω) is a separable, reflexive Banach space, it should be noted that f (•) = 1 2 • 2 H −1 is Gateaux differentiable. Note that the third condition in (37) gives (−∆) −1 U = −p. Thus from (37), it follows that the adjoint variables (p, ϕ) satisfy the following adjoint system in the abstract form:…”

Section: Definition 31 (Admissible Class) the Admissible Classmentioning

confidence: 99%

“…The authors in [3] developed a numerical approach for solving the tidal dynamics problem, based on the splitting methods and the optimal control theory. The global solvability results for stochastic perturbations in bounded and unbounded domains, and asymptotic analysis of solutions is available in [2,16,24,37,40] etc.…”

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confidence: 99%

First order necessary conditions of optimality for the two dimensional tidal dynamics system

Mohan¹

2021

MCRF

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<p style='text-indent:20px;'>In this work, we consider the two dimensional tidal dynamics equations in a bounded domain and address some optimal control problems like total energy minimization, minimization of dissipation of energy of the flow, etc. We also examine an another interesting control problem which is similar to that of the data assimilation problems in meteorology of obtaining unknown initial data, when the system under consideration is the tidal dynamics, using optimal control techniques. For these cases, different distributed optimal control problems are formulated as the minimization of suitable cost functionals subject to the controlled two dimensional tidal dynamics system. The existence of an optimal control as well as the first order necessary conditions of optimality for such systems are established and the optimal control is characterized via the adjoint variable. We also establish the uniqueness of optimal control in small time interval.</p>

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“…see [20], [30], and the references therein. We are interested in the LDP for the family u ε = G ε (W (•)).…”

Section: The Ldpmentioning

confidence: 99%

“…In [6], Budhiraja and Dupuis established a variational representation for positive functionals of Brownian motion applicable to the study of large deviations for a variety of differential equations. It is consequential to exert the variational representation technique to study the large deviations for solution processes of SDEs (see [26] and [30]) and indeed the main result to be established in this paper relies on this technique.…”

Section: Introductionmentioning

confidence: 99%