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Local attractivity in nonautonomous semilinear evolution equations

Joël Blot, Constantin Buşe, Philippe Cieutat (2014)

Nonautonomous Dynamical Systems

We study the local attractivity of mild solutions of equations in the form u’(t) = A(t)u(t) + f (t, u(t)), where A(t) are (possible) unbounded linear operators in a Banach space and where f is a (possible) nonlinear mapping. Under conditions of exponential stability of the linear part, we establish the local attractivity of various kinds of mild solutions. To obtain these results we provide several results on the Nemytskii operators on the space of the functions which converge to zero at infinity...

Local boundedness for minimizers of variational integrals under anisotropic nonstandard growth conditions

Zesheng Feng, Aiping Zhang, Hongya Gao (2024)

Czechoslovak Mathematical Journal

This paper deals with local boundedness for minimizers of vectorial integrals under anisotropic growth conditions by using De Giorgi’s iterative method. We consider integral functionals with the first part of the integrand satisfying anisotropic growth conditions including a convex nondecreasing function g , and with the second part, a convex lower order term or a polyconvex lower order term. Local boundedness of minimizers is derived.

Local center manifold for parabolic equations with infinite delay

Hana Petzeltová (1994)

Mathematica Bohemica

The existence and attractivity of a local center manifold for fully nonlinear parabolic equation with infinite delay is proved with help of a solutions semigroup constructed on the space of initial conditions. The result is applied to the stability problem for a parabolic integrodifferential equation.

Local Collapses in the Truscott-Brindley Model

I. Siekmann, H. Malchow (2008)

Mathematical Modelling of Natural Phenomena

Relaxation oscillations are limit cycles with two clearly different time scales. In this article the spatio-temporal dynamics of a standard prey-predator system in the parameter region of relaxation oscillation is investigated. Both prey and predator population are distributed irregularly at a relatively high average level between a maximal and a minimal value. However, the slowly developing complex pattern exhibits a feature of “inverse excitability”: Both populations show collapses which occur...

Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations

Jean-Michel Coron (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a 1-D tank containing an inviscid incompressible irrotational fluid. The tank is subject to the control which consists of horizontal moves. We assume that the motion of the fluid is well-described by the Saint–Venant equations (also called the shallow water equations). We prove the local controllability of this nonlinear control system around any steady state. As a corollary we get that one can move from any steady state to any other steady state.

Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations

Jean-Michel Coron (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a 1-D tank containing an inviscid incompressible irrotational fluid. The tank is subject to the control which consists of horizontal moves. We assume that the motion of the fluid is well-described by the Saint–Venant equations (also called the shallow water equations). We prove the local controllability of this nonlinear control system around any steady state. As a corollary we get that one can move from any steady state to any other steady state.

Local Discontinuous Galerkin methods for fractional diffusion equations

W. H. Deng, J. S. Hesthaven (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider the development and analysis of local discontinuous Galerkin methods for fractional diffusion problems in one space dimension, characterized by having fractional derivatives, parameterized by β ∈[1, 2]. After demonstrating that a classic approach fails to deliver optimal order of convergence, we introduce a modified local numerical flux which exhibits optimal order of convergence 𝒪(hk + 1) uniformly across the continuous range between pure advection (β = 1) and pure diffusion...

Local energy decay for several evolution equations on asymptotically euclidean manifolds

Jean-François Bony, Dietrich Häfner (2012)

Annales scientifiques de l'École Normale Supérieure

Let  P be a long range metric perturbation of the Euclidean Laplacian on  ℝ d , d ≥ 2 . We prove local energy decay for the solutions of the wave, Klein-Gordon and Schrödinger equations associated to  P . The problem is decomposed in a low and high frequency analysis. For the high energy part, we assume a non trapping condition. For low (resp. high) frequencies we obtain a general result about the local energy decay for the group e i t f ( P ) where f has a suitable development at zero (resp. infinity).

Local Energy Decay in Even Dimensions for the Wave Equation with a Time-Periodic Non-Trapping Metric and Applications to Strichartz Estimates

Kian, Yavar (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 35B40, 35L15.We obtain local energy decay as well as global Strichartz estimates for the solutions u of the wave equation ∂t2 u-divx(a(t,x)∇xu) = 0, t ∈ R, x ∈ Rn, with time-periodic non-trapping metric a(t,x) equal to 1 outside a compact set with respect to x. We suppose that the cut-off resolvent Rχ(θ) = χ(U(T, 0)− e−iθ)−1χ, where U(T, 0) is the monodromy operator and T the period of a(t,x), admits an holomorphic continuation to {θ ∈ C : Im(θ) ≥ 0}, for...

Currently displaying 361 – 380 of 555