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Chunlai Mu,Dengming Liu,Shouming Zhou 대한수학회 2010 대한수학회지 Vol.47 No.6
In this paper, we study the properties of positive solutions for the reaction-diffusion equation [수식] with nonlocal nonlinear boundary condition u (x, t) =∫Ω∫ (x, y) ul (y, t)dy on □Ω×(0, T) and nonnegative initial data u0 (x), where p, q, k, l > 0. Some conditions for the existence and nonexistence of global positive solutions are given.
Mu, Chunlai,Liu, Dengming,Zhou, Shouming Korean Mathematical Society 2010 대한수학회지 Vol.47 No.6
In this paper, we study the properties of positive solutions for the reaction-diffusion equation $u_t$ = $\Delta_u+{\int}_\Omega u^pdx-ku^q$ in $\Omega\times(0,T)$ with nonlocal nonlinear boundary condition u (x, t) = ${\int}_{\Omega}f(x,y)u^l(y,t)dy$ $\partial\Omega\times(0,T)$ and nonnegative initial data $u_0$ (x), where p, q, k, l > 0. Some conditions for the existence and nonexistence of global positive solutions are given.
Influencing Factors of Research Collaboration Intention in Virtual Academic Communities in China
Yan, Chunlai,Li, Hongxia Korea Institute of Science and Technology Informat 2021 Journal of Information Science Theory and Practice Vol.9 No.2
Research collaboration is an important strategy to improve research output, and virtual academic communities (VACs) have become an important platform to collaborate on. This paper reveals the influencing factors of researchers' collaboration intention in VACs from two attributes: individual, and inter-members. On the basis of the Social Cognitive Theory, Social Exchange Theory, social network theory, and Five-Factor Model, this paper constructed a model demonstrating the influencing factors of VACs researchers' collaboration intention. A self-administered questionnaire was employed on members of four VACs in China to collect data; subsequently, 558 usable responses were analyzed using structural equation modeling. The result showed that openness, conscientiousness, reciprocity, trust, and the social network characteristic had a significant influence on the collaboration intention of researchers in VACs, while self-efficacy, agreeableness, extroversion, neuroticism, and experience had no significant effects on the collaboration intention of researchers in VACs. This model plays a positive role in promoting the research collaboration intention of Chinese VACs researchers and in guiding the construction of VAC platforms.
Optimal pre-conditioning and support designs of floor heave in deep roadways
Wang, Chunlai,Li, Guangyong,Gao, Ansen,Shi, Feng,Lu, Zhijiang,Lu, Hui Techno-Press 2018 Geomechanics & engineering Vol.14 No.5
In order to reduce deformation of roadway floor heave in deep underground soft rockmass, four support design patterns were analyzed using the Fast Lagrangian Analysis of Continua (FLAC)3D, including the traditional bolting (Design 1), the bolting with the backbreak in floor (Design 2), the full anchorage bolting with the backbreak in floor (Design 3) and the full anchorage bolting with the bolt-grouting backbreak in floor (Design 4). Results show that the design pattern 4, the full anchorage bolting with the bolt-grouting backbreak in floor, was the best one to reduce the deformation and failure of the roadway, the floor deformation was reduced at 88.38% than the design 1, and these parameters, maximum vertical stress, maximum horizontal displacement and maximum horizontal stress, were greater than 1.69%, 5.96% and 9.97%. However, it was perfectly acceptable with the floor heave results. The optimized design pattern 4 provided a meaningful and reliable support for the roadway in deep underground coal mine.
Experimental investigation of predicting rockburst using Bayesian model
Wang, Chunlai,Chuai, Xiaosheng,Shi, Feng,Gao, Ansen,Bao, Tiancai Techno-Press 2018 Geomechanics & engineering Vol.15 No.6
Rockbursts, catastrophic events involving the violent release of elastic energy stored in rock features, remain a worldwide challenge for geoengineering. Especially at deep-mining sites, rockbursts can occur in hard, high-stress, brittle rock zones, and the associated risk depends on such factors as mining activity and the stress on surrounding rocks. Rockbursts are often sudden and destructive, but there is still no unified standard for predicting them. Based on previous studies, a new Bayesian multi-index model was introduced to predict and evaluate rockbursts. In this method, the rock strength index, energy release index, and surrounding rock stress are the basic factors. Values from 18 rock samples were obtained, and the potential rockburst risks were evaluated. The rockburst tendencies of the samples were modelled using three existing methods. The results were compared with those obtained by the new Bayesian model, which was observed to predict rockbursts more effectively than the current methods.
Critical blow-up and extinction exponents for non-Newton polytropic filtration equation with source
Jun Zhou,Chunlai Mu 대한수학회 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∈(0,+∞) with q1 < q2. In other words, when q belongs to different intervals (0, q_1), (q_1, q_2), (q2,+∞), 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∈(q_2,+∞), there exist both global solutions and blow-up solutions. As for the extinction exponent, the extinction case happens to the interval (q_1,+∞), while for q ∈ (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 λ will play an important role. In other words, when λ belongs to different interval (0, λ_1) or (λ_1,+∞), where λ_1 is the first eigenvalue of p-Laplacian equation with zero boundary value condition, the solution has completely different properties. 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∈(0,+∞) with q1 < q2. In other words, when q belongs to different intervals (0, q_1), (q_1, q_2), (q2,+∞), 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∈(q_2,+∞), there exist both global solutions and blow-up solutions. As for the extinction exponent, the extinction case happens to the interval (q_1,+∞), while for q ∈ (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 λ will play an important role. In other words, when λ belongs to different interval (0, λ_1) or (λ_1,+∞), where λ_1 is the first eigenvalue of p-Laplacian equation with zero boundary value condition, the solution has completely different properties.
Critical Fujita exponent for a fast diffusive equation with variable coefficients
Zhongping Li,Chunlai Mu,Wanjuan Du 대한수학회 2013 대한수학회보 Vol.50 No.1
Abstract. In this paper, we consider the positive solution to a Cauchy problem in RN of the fast diffusive equation: [수식], with nontrivial, nonnegative initial data. Here [수식}. We prove that [수식] is the critical Fujita exponent. That is, if 1 < q ≤ qc, then every positive solution blows up in finite time, but for q > qc, there exist both global and non-global solutions to the problem.
CRITICAL EXPONENTS FOR A DOUBLY DEGENERATE PARABOLIC SYSTEM COUPLED VIA NONLINEAR BOUNDARY FLUX
Yongsheng Mi,Chunlai Mu,Botao Chen 대한수학회 2011 대한수학회지 Vol.48 No.3
The paper deals with the degenerate parabolic system with nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve. The critical Fujita curve is conjectured with the aid of some new results.