Localized peaking regimes for quasilinear parabolic equations

This paper deals with the asymptotic behavior as of all weak (energy) solutions of a class of equations with the following model representative: with prescribed global energy function Here , , , Ω is a bounded smooth domain, . Particularly, in the case it is proved that the solution u remains uniformly bounded as in an arbitrary subdomain and the sharp upper estimate of when has been obtained depending on and . In the case for all , sharp sufficient conditions on degeneration of near that guarantee the above mentioned boundedness for an arbitrary (even large) solution have been found and the sharp upper estimate of a final profile of the solution when has been obtained.     

Rapid Detection of Serum Procalcitonin by Immunochromatograghy Technology Based on Freeze‐dried Up‐conversion Nanoparticles/Antibody Conjugates

Procalcitonin (PCT) is a sensitive and specific biomarker for sepsis diagnosis and widely used as a biomarker to improve the diagnosis of bacterial infections and to guide the antibiotic therapy. In our work, an improved up‐converting nanoparticle (UCP) technology based on the immunochromatographic assay (UPT‐ICA) was developed for rapid and quantitative detection of PCT. In order to further improve the accuracy, sensitivity and stability of the assay on the basis of our previous study, the UCP coupling with monoclonal antibody of PCT (UCP‐Ab1) was freeze‐dried under certain conditions. And the detections of PCT levels with UCP‐Ab1 conjugates before and after freeze‐drying were evaluated. The results show that, compared to the UCP‐Ab1 conjugates without freeze‐drying, the detection sensitivity of freeze‐dried UCP‐Ab1 is slightly improved, having a lower immunochromatogragh background and better stability. This improved method can provide a rapid, accurate, and relatively easy way for the clinical detection of PCT.     

Asymptotic behavior of the solutions of maxwell—klein—gordon field equations in 4—dimensional minkowski space

Abstract. This paper studies the asymptotic behavior of the solutions of massive coupled Maxwell—Klein—Gordon field equations in the 4—dimensional Minkowski space for the case of small initial data with charge. The proof relies on gauge invariant energy estimates and geometric properties of the fields equations. The presence of charge together with the mass term in the Klein—Gordon equation are the novelties of this project and provide us with a situation which cannot be accomodated by standard methods such as the conformal transformation. A covariant Lie derivative operator for the Klein—Gordon field is introduced and allows us to handle the most troublesome terms in the error estimates.     

Possibility of the existence of blow‐up solutions to quasilinear degenerate Keller–Segel systems of parabolic–parabolic type

This paper deals with the quasilinear ‘degenerate’ Keller–Segel system of parabolic–parabolic type under the super‐critical condition. In the ‘non‐degenerate’ case, Winkler (Math. Methods Appl. Sci. 2010; 33:12–24) constructed the initial data such that the solution blows up in either finite or infinite time. However, the blow‐up under the super‐critical condition is left as an open question in the ‘degenerate’ case. In this paper, we try to give an answer to the question under assuming the existence of local solutions. Copyright © 2012 John Wiley & Sons, Ltd.     

全息波导显示构型设计(英文)

针对全息波导显示系统中输入光栅、转折光栅和输出光栅的光栅参量不一致,导致系统设计和光栅制作难度增大的问题.对比正常配置和锥形配置下的光栅方程,可得全息波导显示系统中全息光栅具有相同周期需要满足转向光栅60°锥形配置.由此提出波导侧面装有反射镜的三光栅单波导板显示构型,其中三个光栅周期完全相同,输入光栅和转向光栅条纹走向一致.使用光学设计软件CODE V对该构型进行仿真,验证了该构型的可行性.与传统全息波导显示构型相比,侧面反射镜的光路折叠作用使得该构型系统无效显示面积和耦合效率损失减小;三个光栅周期相同且输入光栅和转向光栅条纹走向一致,可以降低系统设计和全息光栅制作难度.该构型可以用于虚拟现实显示或者头戴式显示.     

Blow‐up phenomena for a pseudo‐parabolic equation

By the means of a differential inequality technique, we obtain a lower bound for blow‐up time if p and the initial value satisfy some conditions. Also, we establish a blow‐up criterion and an upper bound for blow‐up time under some conditions as well as a nonblow‐up and exponential decay under some other conditions. Copyright © 2014 John Wiley & Sons, Ltd.     

A Fourier pseudospectral method for a generalized improved Boussinesq equation

In this article, we propose a Fourier pseudospectral method for solving the generalized improved Boussinesq equation. We prove the convergence of the semi‐discrete scheme in the energy space. For various power nonlinearities, we consider three test problems concerning the propagation of a single solitary wave, the interaction of two solitary waves and a solution that blows up in finite time. We compare our numerical results with those given in the literature in terms of numerical accuracy. The numerical comparisons show that the Fourier pseudospectral method provides highly accurate results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 995–1008, 2015     

Invariant sets and the blow up threshold for coupled systems of reaction–diffusion

In this paper, we study a class of semilinear systems of reaction–diffusion on a bounded smooth domain with Dirichlet boundary condition. Applying the potential well method, we find invariant sets for the initial-boundary value problem and derive a threshold of blow up and global existence for its solution.