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Low-Dimensional Description of Pulses under the Action of Global Feedback Control

Y. Kanevsky, A. A. Nepomnyashchy (2012)

Mathematical Modelling of Natural Phenomena

The influence of a global delayed feedback control which acts on a system governed by a subcritical complex Ginzburg-Landau equation is considered. The method based on a variational principle is applied for the derivation of low-dimensional evolution models. In the framework of those models, one-pulse and two-pulse solutions are found, and their linear stability analysis is carried out. The application of the finite-dimensional model allows to reveal...

Lower bounds for pseudo-differential operators

C. Fefferman, D. H. Phong (1981/1982)

Séminaire Équations aux dérivées partielles (Polytechnique)

Lp estimates for degenerate elliptic equations.

Antonio Sánchez-Calle (1988)

Revista Matemática Iberoamericana

In this note we are going to address the question of when a second order differential operator is controlled by a subelliptic second order differential operator.

Lp - Lp'-Estimates for Fourier Integral Operators Related to Hyperbolic Equations.

Philip Brenner (1976/1977)

Mathematische Zeitschrift

Lp regularity of the Dirichlet problem for elliptic equations with singular drift.

Cristian Rios (2006)

Publicacions Matemàtiques

Lp-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen. I.

Hartmut Pecher (1976)

Mathematische Zeitschrift

Lp-Decacy Rates for Homogeneous Wave-Equations.

Wolf von Wahl (1971)

Mathematische Zeitschrift

Lq - Lr estimates for solutions of the nonstationary Stokes equations in an exterior domain and the Navier-Stokes initial value problems in Lq spaces.

Hirokazu Iwashita (1989)

Mathematische Annalen

Lyapunov center theorem for some nonlinear PDE's : a simple proof

Dario Bambusi (2000)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Lyapunov control of a quantum particle in a decaying potential

Mazyar Mirrahimi (2009)

Annales de l'I.H.P. Analyse non linéaire

Lyapunov functions and $L^{p}$ -estimates for a class of reaction-diffusion systems

Dirk Horstmann (2001)

Colloquium Mathematicae

We give a sufficient condition for the existence of a Lyapunov function for the system aₜ = ∇(k(a,c)∇a - h(a,c)∇c), x ∈ Ω, t > 0, $ε c ₜ = k_{c} Δ c - f (c) c + g (a, c)$ , x ∈ Ω, t > 0, for $Ω \subset ℝ^{N}$ , completed with either a = c = 0, or ∂a/∂n = ∂c/∂n = 0, or k(a,c) ∂a/∂n = h(a,c) ∂c/∂n, c = 0 on ∂Ω × t > 0. Furthermore we study the asymptotic behaviour of the solution and give some uniform $L^{p}$ -estimates.

Lyapunov Functions for Weak Solutions of Reaction-Diffusion Equations with Discontinuous Interaction Functions and its Applications

Mark O. Gluzman, Nataliia V. Gorban, Pavlo O. Kasyanov (2015)

Nonautonomous Dynamical Systems

In this paper we investigate additional regularity properties for global and trajectory attractors of all globally defined weak solutions of semi-linear parabolic differential reaction-diffusion equations with discontinuous nonlinearities, when initial data uτ ∈ L2(Ω). The main contributions in this paper are: (i) sufficient conditions for the existence of a Lyapunov function for all weak solutions of autonomous differential reaction-diffusion equations with discontinuous and multivalued interaction...

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