This paper gives a systematic treatment of two methods for obtaining operator estimates: the
shift method and the spectral method. Though substantially different in mathematical …

В работе дано систематическое изложение двух методов получения операторных
оценок: метода сдвига и спектрального метода. Эти методы сильно различаются по …

We show that a twist of a three-dimensional tube of uniform cross-section yields an improved
decay rate for the heat semigroup associated with the Dirichlet Laplacian in the tube. The …

The authors study the asymptotic behaviour of solutions of the heat equation and a number
of evolution equations using scaling techniques. It is proved that in the framework of …

We prove local and global energy decay for the asymptotically periodic damped wave
equation on the Euclidean space. Since the behavior of high frequencies is already mostly …

ASYMPTOTIC EXPANSION FOR DAMPED WAVE EQUATIONS WITH PERIODIC
COEFFICIENTS Page 1 September 10, 2001 15:44 WSPC/103-M3AS 00133 Mathematical …

In this work, decay estimates are derived for the solutions of 1-D linear parabolic PDEs with
disturbances at both boundaries and distributed disturbances. The decay estimates are …

We consider dissipative systems on the real axis in situations when the evolution is
dominated by a dynamics similar to the one of a linear diffusion equation. It is surprising that …

Abstract In L 2 (R 3; C 3), we consider a selfadjoint operator L ε, ε> 0, given by the differential
expression μ− 1/2 curl η (x/ε)− 1 curl μ− 1/2− μ 1/2∇ ν (x/ε) div μ 1/2, where μ is a constant …

We consider in this paper a general reaction-diffusion equation of the KPP (Kolmogorov,
Petrovskiĭ, Piskunov) type, posed on an infinite cylinder. Such a model will have a family of …