A Higher-Order Energy Expansion to Two-Dimensional Singularly Neumann Problems [PDF]
, 2005 Of concern is the following singularly perturbed semilinear elliptic problem \begin{equation*} \left\{ \begin{array}{c} \mbox{${\epsilon}^2\Delta u -u+u^p =0$ in $\Omega$}\\ \mbox{$u>0$ in $\Omega$ and $
Yeung, W-K, Winter, M, Wei, J
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Maximum norm a posteriori error estimate for a 2d singularly perturbed semilinear reaction-diffusion problem [PDF]
, 2008 A singularly perturbed semilinear reaction-diffusion equation, posed in the unit square, is discretized on arbitrary nonuniform tensor-product meshes. We establish a second-order maximum norm a posteriori error estimate that holds true uniformly in the ...
Kopteva, Natalia
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Maximum norm a posteriori error estimation for parabolic problems using elliptic reconstructions [PDF]
, 2013 A semilinear second-order parabolic equation is considered in a regular and a singularly perturbed regime. For this equation, we give computable a posteriori error estimates in the maximum norm.
Linss, Torsten, Kopteva, Natalia
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The linear quadratic regulator problem for a class of controlled systems modeled by singularly perturbed Ito differential equations [PDF]
, 2012 Link to a related website: https://digital.library.adelaide.edu.au/dspace/bitstream/2440/77907/1/hdl_77907.pdf, Open Access via UnpaywallThis paper discusses an infinite-horizon linear quadratic (LQ) optimal control problem involving state- and control ...
Shi, Peng +5 more
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A Singularly Perturbed System of Parabolic Equations
Lobachevskii Journal of Mathematics, 2021 The work is devoted to the construction of the asymptotic behavior of the solution of a singularly perturbed system of equations of parabolic type, in the case when the limit equation has a regular singularity as the small parameter tends to zero. The asymptotics of the solution of such problems contains boundary layer functions.
Omuraliev, A. S., Esengul kyzy, P.
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Critical Threshold and Stability of Cluster Solutions for Large Reaction-Diffusion Systems in R [PDF]
, 2002 We study a large reaction-diffusion system which arises in the modeling of catalytic networks and describes the emerging of cluster states. We construct single cluster solutions on the real line and then establish their stability or instability in
Winter, M, Wei, J
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Exponential stability for singularly perturbed systems with state delays
Electronic Journal of Qualitative Theory of Differential Equations, 2000 In this paper the problem of stability of the zero solution of singularly perturbed system of linear differential equation with state delays is investigated.
V. Dragan, A. Ionita
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Event‐triggered control of singularly perturbed linear system with DoS attacks
IET Control Theory & Applications, 2021 This paper presents the event‐triggered control problem of linear singularly perturbed systems in the presence of denial‐of‐service attacks. To save the communication and computing resources, event‐triggered mechanisms in two transmission channels are ...
Xiang Ren, Fei Hao
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Multi-Objective Optimal Control for Uncertain Singularly Perturbed Systems
IEEE Access, 2021 This paper studies the passive multi-objective optimal control of uncertain singularly perturbed systems. First, the uncertainty is described in a norm-bounded way, and then the state space model of the system is determined.
Lei Liu, Shaofan Feng
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Higher order energy expansions for some singularly perturbed Neumann problems [PDF]
, 2003 We consider the following singularly perturbed semilinear elliptic problem: \epsilon^{2} \Delta u - u + u^p=0 \ \ \mbox{in} \ \Omega, \quad u>0 \ \ \mbox{in} \ \ \Omega \quad \mbox{and} \ \frac{\partial u}{\partial \nu} =0 \ \mbox{on} \ \partial \
Winter, M +5 more
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