Lijuan Wang’s research while affiliated with Wuhan University and other places

... The plan of the proof of Lemma 1, inspired by the ideas presented in [14,16,30], is outlined as follows. In Step 1, we perform a change of function and introduce both the symmetric and antisymmetric parts. ...

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Null Approximate Impulse Controllability for a Degenerate Parabolic Equation in Non Divergence Form with Drift

... There are many interesting works about norm optimal control problems governed by evolution equations (see, for instance, [10], [9], [7], [15], [14], [6], [16]). Most of them are mainly concerned with two topics: characterization of norm optimal controls, and connections between minimal (or maximal) time controls and the minimal norm controls. ...

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Convergence of minimal norm control problems of linear heat equations with time delay

... On the one side, we want to avoid chaos in some fields of engineering for its characteristic. On the other side, chaotic property can be applied in secure communication in order to enhance the security of information [1][2][3][4][5]. These extensive and deep researches lead to a large number of areas of implementation related to nonlinear systems with chaotic characteristic. ...

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A new four-dimensional memristive system, synchronization and its application in image encryption

... In [20], the authors proved that the unique continuation estimate for the pure heat equation in R n holds if and only if the unbounded observable set is thick set. In [21,22], the authors proved a global interpolation inequality for solutions of the heat equation with bounded potential at one point of time variable using the parabolic-type frequency function method. In [23], the authors proved a Hölder-type interpolation inequalities of unique continuation for fractional order parabolic equations with space-time dependent potentials on a thick set. ...

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Quantitative uniqueness estimates for stochastic parabolic equations on the whole Euclidean space

... where α and β are two constants. By similar arguments as those in [16] (see the proof of (3.17) in [16]), we can directly check that (H) holds. ...

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Equivalence of three kinds of optimal control problems for linear heat equations with memory

... For such an ideal state, it is necessary to study dynamical systems with discontinuous trajectories, which can also be called impulsive dynamic systems. In recent years, due to the needs of modern technology, impulsive control system and impulsive perturbation system have attracted more and more attention, and the application of impulse dynamical system in technical problems is increasingly extensive, such as [33,7,39,37,3,28,30,34,29,26]. As is known to all that time delay is ubiquitous in dynamical systems and engineering applications. ...

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Stability of Time-Delay Systems with Delayed Impulses: Average Impulsive Estimation Approach

... In fact, the theory of minimum time impulse controls has been extensively used in various practical mathematical models, and has become an important research field in recent years. This can be found in a large number of literature (see [1,4,7,11,12,15,16,21,23,26,28,31]). ...

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Minimal Time Impulse Control for a Class of Homogeneous Evolution Equations

... This question is motivated by the literature [14], which studies a similar equation in a bounded convex domain. Extensive related references can be found in [2,5,9,13] and the rich works cited therein. Reference [16] studies the relationship between the observation region and observability for the linear heat equation in R n and shows that an observation region satisfies the observability inequality if and only if it is γ−thick at scale L for some γ > 0 and L > 0. To study this problem, we need to characterize suitable conditions for the observation region ω. ...

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Observation estimates for a semilinear heat equation in \mathbb{R}^n

... For time-dependent systems, the control problem (1.1)-(1.2) posed in M(Ī c ; L 2 (ω)) yields controls with compact support in time. This characteristic allows for determining the optimal moments for control device actions, akin to a generalization of impulse control [31][32][33][34][35][36][37][38][39][40][41]. Recall that in impulse control problems, the control q in (1.1)-(1.2) is replaced by ...

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Analysis and approximation to parabolic optimal control problems with measure-valued controls in time

... For time-dependent systems, the control problem (1.1)-(1.2) posed in M(Ī c ; L 2 (ω)) yields controls with compact support in time. This characteristic allows for determining the optimal moments for control device actions, akin to a generalization of impulse control [31][32][33][34][35][36][37][38][39][40][41]. Recall that in impulse control problems, the control q in (1.1)-(1.2) is replaced by ...

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Analysis and approximation to parabolic optimal control problems with measure-valued controls in time