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BLOW-UP FOR A NON-NEWTON POLYTROPIC FILTRATION SYSTEM WITH NONLINEAR NONLOCAL SOURCE
Zhou, Jun,Mu, Chunlai Korean Mathematical Society 2008 대한수학회논문집 Vol.23 No.4
This paper deals the global existence and blow-up properties of the following non-Newton polytropic filtration system, $${u_t}-{\triangle}_{m,p}u=u^{{\alpha}_1}\;{\int}_{\Omega}\;{\upsilon}^{{\beta}_1}\;(x,\;t)dx,\;{\upsilon}_t-{\triangle}_{n,p}{\upsilon}={\upsilon}^{{\alpha}_2}\;{\int}_{\Omega}\;u^{{\beta}_2}\;(x,{\;}t)dx,$$ with homogeneous Dirichlet boundary condition. Under appropriate hypotheses, we prove that the solution either exists globally or blows up in finite time depends on the initial data and the relations of the parameters in the system.
CRITICAL BLOW-UP AND EXTINCTION EXPONENTS FOR NON-NEWTON POLYTROPIC FILTRATION EQUATION WITH SOURCE
Zhou, Jun,Mu, Chunlai Korean Mathematical Society 2009 대한수학회보 Vol.46 No.6
This paper deals with the critical blow-up and extinction exponents for the non-Newton polytropic filtration equation. We reveals a fact that the equation admits two critical exponents $q_1,\;q_2\;{\in}\;(0,+{\infty})$) with $q_1\;{<}\;q_2$. In other words, when q belongs to different intervals (0, $q_1),\;(q_1,\;q_2),\;(q_2,+{\infty}$), the solution possesses complete different properties. More precisely speaking, as far as the blow-up exponent is concerned, the global existence case consists of the interval (0, $q_2$]. However, when q ${\in}\;(q_2,+{\infty}$), there exist both global solutions and blow-up solutions. As for the extinction exponent, the extinction case happens to the interval ($q_1,+{\infty}$), while for q ${\in}\;(0,\;q_1$), there exists a non-extinction bounded solution for any nonnegative initial datum. Moreover, when the critical case q = $q_1$ is concerned, the other parameter ${\lambda}$ will play an important role. In other words, when $\lambda$ belongs to different interval (0, ${\lambda}_1$) or (${\lambda}_1$,+${\infty}$), where ${\lambda}_1$ is the first eigenvalue of p-Laplacian equation with zero boundary value condition, the solution has completely different properties.
Zhou, Jun,Xu, Xiao-Zhen,Hu, Yao-Ren,Hu, Ai-Rong,Zhu, Cheng-Liang,Gao, Guo-Sheng Asian Pacific Journal of Cancer Prevention 2014 Asian Pacific journal of cancer prevention Vol.15 No.6
Cryptotanshinone (CPT), is a quinoid diterpene isolated from the root of the Asian medicinal plant, Salvia miotiorrhiza bunge. Numerous researchers have found that it could work as a potent antitumor agent to inhibit tumor growth in vitro, buith there has been much less emphasis on its in vivo role against breast tumors. Using a mouse tumor model of MCF7 cells, we showed that CPT strongly inhibited MCF7 cell growth in vivo with polarization of immune reactions toward Th1-type responses, stimulation of naive CD4+ T cell proliferation, and also increased IFN-${\gamma}$ and perforin production of CD4+ T cells in response to tumor-activated splenocytes. Furthermore, data revealed that the cytotoxic activity of CD4+ T cells induced by CPT was markedly abrogated by concanamycin A(CMA), a perforin inhibitor, but not IFN-${\gamma}$ Ab. On the other hand, after depletion of CD4+ T cells or blocked perforin with CMA in a tumor-bearing model, CPT could not effectively suppress tumor growth, but this phenomenon could be reversed by injecting naive CD4+ T cells. Thus, our results suggested that CPT mainly inhibited breast tumor growth through inducing cytotoxic CD4+ T cells to secrete perforin. We further found that CPT enhanced perforin production of CD4+ T cells by up-regulating JAK2 and STAT4 phosphorylation. These findings suggest a novel potential therapeutic role for CPT in tumor therapy, and demonstrate that CPT performs its antitumor functions through cytotoxic CD4+ T cells.
Clean Development Mechanism and Its Risk Management Policy in Urban Infrastructure Construction
Zhou Jun,Zhang Hongwei,Liu Yingjia 보안공학연구지원센터 2015 International Journal of Security and Its Applicat Vol.9 No.7
Clean Development Mechanism (CDM) is a multi-win solution for the low-carbon development of urban infrastructure. It provides a low-cost plan and offering channels for technical transformation. Moreover, effective clean development strategy can certainly produce additional capital and technology benefits to meet the requirements of sustainability for urban infrastructure construction. This paper illustrates the clean development principles of urban infrastructure in a broader sense,and pay attention to the potential risk and controlling methodology of the CDM, which aims at promoting the formation and positive development of urban CMD system.
PATTERN FORMATION IN A GENERAL DEGN-HARRISON REACTION MODEL
Zhou, Jun Korean Mathematical Society 2017 대한수학회보 Vol.54 No.2
In this paper, we study the pattern formation to a general Degn-Harrison reaction model. We show Turing instability happens by analyzing the stability of the unique positive equilibrium with respect to the PDE model and the corresponding ODE model, which indicate the existence of the non-constant steady state solutions. We also show the existence periodic solutions of the PDE model and the ODE model by using Hopf bifurcation theory. Numerical simulations are presented to verify and illustrate the theoretical results.
BIFURCATION ANALYSIS OF A SINGLE SPECIES REACTION-DIFFUSION MODEL WITH NONLOCAL DELAY
Zhou, Jun Korean Mathematical Society 2020 대한수학회지 Vol.57 No.1
A reaction-diffusion model with spatiotemporal delay modeling the dynamical behavior of a single species is investigated. The parameter regions for the local stability, global stability and instability of the unique positive constant steady state solution are derived. The conditions of the occurrence of Turing (diffusion-driven) instability are obtained. The existence of time-periodic solutions, the existence and nonexistence of nonconstant positive steady state solutions are proved by bifurcation method and energy method. Numerical simulations are presented to verify and illustrate the theoretical results.