scholarly journals Asymptotics of the principal eigenvalue for a linear time-periodic parabolic operator II: Small diffusion

2020 ◽  
pp. 1
Author(s):  
Shuang Liu ◽  
Yuan Lou ◽  
Rui Peng ◽  
Maolin Zhou
Keyword(s):  
Linear Time ◽  
Principal Eigenvalue ◽  
Parabolic Operator ◽  
Small Diffusion ◽  
Time Periodic

scholarly journals Monotonicity of the principal eigenvalue for a linear time-periodic parabolic operator

2019 ◽  
Vol 147 (12) ◽  
pp. 5291-5302 ◽  
Author(s):  
Shuang Liu ◽  
Yuan Lou ◽  
Rui Peng ◽  
Maolin Zhou
Keyword(s):  
Linear Time ◽  
Principal Eigenvalue ◽  
Parabolic Operator ◽  
Time Periodic

Protection Zones in Periodic-Parabolic Problems

2020 ◽  
Vol 20 (2) ◽  
pp. 253-276
Author(s):  
Julián López-Gómez
Keyword(s):  
Mixed Type ◽  
Principal Eigenvalue ◽  
Boundary Operator ◽  
General Boundary ◽  
Parabolic Problems ◽  
Parabolic Operator ◽  
Protection Zones ◽  
Competitive Environments

AbstractThis paper characterizes whether or not\Sigma_{\infty}\equiv\lim_{\lambda\uparrow\infty}\sigma[\mathcal{P}+\lambda m(% x,t),\mathfrak{B},Q_{T}]is finite, where {m\gneq 0} is T-periodic and {\sigma[\mathcal{P}+\lambda m(x,t),\mathfrak{B},Q_{T}]} stands for the principal eigenvalue of the parabolic operator {\mathcal{P}+\lambda m(x,t)} in {Q_{T}\equiv\Omega\times[0,T]} subject to a general boundary operator of mixed type, {\mathfrak{B}}, on {\partial\Omega\times[0,T]}. Then this result is applied to discuss the nature of the territorial refuges in periodic competitive environments.

scholarly journals Linear Time-Periodic System Identification with Grouped Atomic Norm Regularization

2020 ◽  
Vol 53 (2) ◽  
pp. 1237-1242
Author(s):  
Mingzhou Yin ◽  
Andrea Iannelli ◽  
Mohammad Khosravi ◽  
Anilkumar Parsi ◽  
Roy S. Smith
Keyword(s):  
System Identification ◽  
Periodic System ◽  
Linear Time ◽  
Atomic Norm ◽  
Time Periodic

Metastability for a generalized Burgers equation with applications to propagating flame fronts

1999 ◽  
Vol 10 (1) ◽  
pp. 27-53 ◽  
Author(s):  
X. SUN ◽  
M. J. WARD
Keyword(s):  
Flame Front ◽  
Principal Eigenvalue ◽  
Vertical Channel ◽  
Front Propagation ◽  
Slow Motion ◽  
Diffusion Limit ◽  
Asymptotic Results ◽  
Small Diffusion ◽  
Generalized Burgers Equation ◽  
Exponentially Small

In the small diffusion limit ε→0, metastable dynamics is studied for the generalized Burgers problemformula hereHere u=u(x, t) and f(u) is smooth, convex, and satisfies f(0)=f′(0)=0. The choice f(u)=u2/2 has been shown previously to arise in connection with the physical problem of upward flame-front propagation in a vertical channel in a particular parameter regime. In this context, the shape y=y(x, t) of the flame-front interface satisfies u=−yx. For this problem, it is shown that the principal eigenvalue associated with the linearization around an equilibrium solution corresponding to a parabolic-shaped flame-front interface is exponentially small. This exponentially small eigenvalue then leads to a metastable behaviour for the time- dependent problem. This behaviour is studied quantitatively by deriving an asymptotic ordinary differential equation characterizing the slow motion of the tip location of a parabolic-shaped interface. Similar metastability results are obtained for more general f(u). These asymptotic results are shown to compare very favourably with full numerical computations.

Periodic controller for guaranteed simultaneous stabilization of two plants with robust zero error tracking

2018 ◽  
Vol 233 (5) ◽  
pp. 480-490
Author(s):  
Arindam Chakraborty ◽  
Jayati Dey
Keyword(s):  
Design Methodology ◽  
Linear Time ◽  
Pole Placement ◽  
Control Input ◽  
Efficient Design ◽  
Simultaneous Stabilization ◽  
Bounded Control ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
Time Periodic

The guaranteed simultaneous stabilization of two linear time-invariant plants is achieved by continuous-time periodic controller with high controller frequency. Simultaneous stabilization is accomplished by means of pole-placement along with robust zero error tracking to either of two plants. The present work also proposes an efficient design methodology for the same. The periodic controller designed and synthesized for realizable bounded control input with the proposed methodology is always possible to implement with guaranteed simultaneous stabilization for two plants. Simulation and experimental results establish the veracity of the claim.

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