Homogenization limit of a parabolic equation with nonlinear boundary conditions

Consider the parabolic equation

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Superstability and rigorous asymptotics in singularly perturbed state-dependent delay-differential equations

We study the singularly perturbed state-dependent delay-differential equation

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The asymptotic behaviour of the heat equation in a twisted Dirichlet-Neumann waveguide

We consider the heat equation in a straight strip, subject to a combination of Dirichlet and Neumann boundary conditions. We show that a switch of the respective boundary conditions leads to an improvement of the decay rate of the heat semigroup of the order of t−1/2. The proof employs similarity variables that lead to a non-autonomous parabolic equation in a thin strip contracting to the real line, that can be analysed on weighted Sobolev spaces in which the operators under consideration have discrete spectra. A careful analysis of its asymptotic behaviour shows that an added Dirichlet boundary condition emerges asymptotically at the switching point, breaking the real line in two half-lines, which leads asymptotically to the 1/2 gain on the spectral lower bound, and the t−1/2 gain on the decay rate in the original physical variables.This result is an adaptation to the case of strips with twisted boundary conditions of previous results by the authors on geometrically twisted Dirichlet tubes.     

Homogenization of a parabolic model of ferromagnetism

This work deals with the homogenization of hysteresis-free processes in ferromagnetic composites. A degenerate, quasilinear, parabolic equation is derived by coupling the Maxwell-Ohm system without displacement current with a nonlinear constitutive law:

     

Nonexistence of type II blowup solution for a semilinear heat equation

A solution u of a Cauchy problem for a semilinear heat equation

     

A sufficient condition for type I blowup in a parabolic-elliptic system

This paper is concerned with blowup of positive solutions to a Cauchy problem for a parabolic-elliptic system

     

Applications of hybrid universality to multivariable zeta-functions

In the present paper, we obtain new results on universality as applications of hybrid universality and almost-periodicity in its half-plane of absolute convergence. By using these, we show the universality for Euler products of Igusa type, Euler-Zagier multiple zeta-functions and Tornheim-Hurwitz type of double zeta-functions.     

On consensus speed of multi-agent systems with double-integrator dynamics

The performance of multi-agent systems is an important issue. In this paper, it is focused on consensus speed for multi-agent systems with double-integrator dynamics and fixed undirected graphes under a kind of consensus protocols. It is revealed that, under some conditions, the maximum consensus speed is determined by the largest and the smallest nonzero eigenvalues of the Laplacian matrix of the undirected connected graph. Based on the mentioned results, arbitrary desired consensus speed can be achieved by choosing suitable feedback gains. Numerical simulations are given to illustrate the main results.     

Quantum numerical control for free elementary particle

This work is to survey the quantum control for free elementary particle numerically. Without considering of the magnetic and electronic fields, control theory of nucleus (nucleons and meson) will be proposed. Furthermore, computational approach will be preformed for control landscape in two dimensions (2D) to illustrate the theoretic results.