• 대한수학회논문집
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• 제35권4호
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• pp.1143-1158
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• 2020

In this paper, we are concerned with the blow-up phenomena for a class of pseudo-parabolic equations with weighted source u_t - △u - △u_t = a(x)f(u) subject to Dirichlet (or Neumann) boundary conditions in any smooth bounded domain Ω ⊂ ℝⁿ (n ≥ 1). Firstly, we obtain the upper and lower bounds for blow-up time of solutions to these problems. Moreover, we also give the estimates of blow-up rate of solutions under some suitable conditions. Finally, three models are presented to illustrate our main results. In some special cases, we can even get some exact values of blow-up time and blow-up rate.

• 대한수학회논문집
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• 제27권3호
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• pp.629-644
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• 2012

In this work, the authors study the blow-up properties of solutions to a parabolic system with nonlocal boundary conditions and nonlocal sources. Conditions for the existence of global or blow-up solutions are given. Global blow-up property and precise blow-up rate estimates are also obtained.

• 대한수학회보
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• 제50권6호
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• pp.1765-1780
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• 2013

This paper deals with some types of semilinear parabolic systems with localized or nonlocal sources and nonlocal boundary conditions. The authors first derive some global existence and blow-up criteria. And then, for blow-up solutions, they study the global blow-up property as well as the precise blow-up rate estimates, which has been seldom studied until now.

• 대한수학회보
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• 제52권1호
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• pp.173-182
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• 2015

In this paper, the blow-up rate of $L^2$-norm for the semi-linear wave equation with a power nonlinearity is obtained in the bounded domain for any p > 1. We also get the blow-up rate of the derivative under the condition 1 < p < $1+\frac{4}{N-1}$ for $N{\geq}2$ or 1 < p < 5 for N = 1.

• 대한수학회지
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• 제53권1호
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• pp.27-43
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• 2016

This paper deals with a degenerate parabolic system with coupled nonlinear localized sources subject to weighted nonlocal Dirichlet boundary conditions. We obtain the conditions for global and blow-up solutions. It is interesting to observe that the weight functions for the nonlocal Dirichlet boundary conditions play substantial roles in determining not only whether the solutions are global or blow-up, but also whether the blowing up occurs for any positive initial data or just for large ones. Moreover, we establish the precise blow-up rate.

• Journal of applied mathematics & informatics
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• 제34권5_6호
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• pp.359-367
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• 2016

This paper deals with the Cauchy problem for heat equations with coupling moving reactions of mixed type. After obtaining the infinite Fujita blow-up exponent, we classify optimally the simultaneous and non-simultaneous blow-up for two components of the solutions. Moreover, blow-up rates and set are determined. By using the analogous procedures, one can fill in the gaps for the other two systems, which are studied in the paper 'Australian and New Zealand Industrial and Applied Mathematics Journal' 48(2006)37-56.

• 대한수학회지
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• 제44권4호
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• pp.779-786
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• 2007

In this note, we consider a system of two reaction-diffusion equations with absorption, under homogeneous Dirichlet boundary. Using scaling methods, we establish the blow-up rate estimates.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2009년도 제33회 추계학술대회논문집
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• pp.213-216
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• 2009

가스터빈 연소기의 화염 특성을 알기 위하여 분할 연소기 시험을 수행하였다. 점화시험은 여러 가지 연소기 유입 공기속도와 공기과잉율에 따라 토치 점화장치를 이용하여 수행되었다. 또한, 연료를 충분히 공급한 상태에서 점화를 수행한 후 점차 연료량을 감소시켜가며 희박연소한계를 측정 하였다. 실험 결과, 공기과잉율 6에서 안정한 점화를 보였고 이 값은 연소기 공기 유입속도에 따라 점점 증가함을 보였다. 최소 실화한계는 연소기 공기 유입속도 40 m/s에서 약 4였고, 이 값 또한 연소기공기유입속도에 따라 약 10 까지 증가함을 보였다.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.217-231
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• 2010

We consider a class of elliptic problems of a logistic type $$-div(|{\nabla}_u|^{m-2}{\nabla}_u)\;=\;w(x)u^q\;-\;(a(x))^{\frac{m}{2}}\;f(u)$$ in a bounded domain of $\mathbf{R}^N$ with boundary $\partial\Omega$ of class $C^2$, $u|_{\partial\Omega}\;=\;+{\infty}$, $\omega\;\in\;L^{\infty}(\Omega)$, 0 < q < 1 and $a\;{\in}\;C^{\alpha}(\bar{\Omega})$, $\mathbf{R}^+$ is non-negative for some $\alpha\;\in$ (0,1), where $\mathbf{R}^+\;=\;[0,\;\infty)$. Under suitable growth assumptions on a, b and f, we show the exact blow-up rate and uniqueness of the large solutions. Our proof is based on the method of sub-supersolution.

• 한국추진공학회지
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• 제15권4호
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• pp.11-17
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• 2011

가스터빈 연소기의 화염 특성을 알기 위하여 분할 연소기 시험을 수행하였다. 점화시험은 여러 가지 연소기 유입 공기속도와 공기과잉율에 따라 토치 점화장치를 이용하여 수행되었다. 또한, 연료를 충분히 공급한 상태에서 점화를 수행한 후 점차 연료량을 감소시켜가며 희박연소한계를 측정하였다. 실험결과, 공기과잉율 6에서 안정한 점화를 보였고 이 값은 연소기 공기 유입속도에 따라 점점 증가함을 보였다. 최소 실화한계는 연소기 공기 유입속도 40 m/s 에서 약 4였고, 이 값은 연소기 공기유입속도에 따라 약 10까지 증가함을 보였다. 화염특성 시험결과, 화염안정성은 연소기 유입속도가 커질수록 희박화염소실한계는 넓어짐을 알 수 있었고, 연소기 유입 공기속도가 약 65 m/s 에서 가장 큰 화염소실 한계를 보였다.