具非局部源反应扩散方程组解的同时爆破与不同时爆破

本文讨论具齐次Dirichlet边界条件非局部源反应扩散方程组的爆破解,给出四类同时爆破与不同时爆破现象的判定指标,这四类爆破现象包含:(i)存在不同时爆破;(ii)同时爆破与不同时爆破共存;(iii)任意爆破必是同时爆破;(iv)任意爆破必是不同时爆破.     

异位孔爆破破碎块度与设计孔的分形匹配研究

针对露天矿炮区工作面中穿爆作业不规律导致爆破效果不佳现象,通过在胜利露天矿进行爆破试验得到实测数据,利用分形理论中分维数与爆破破碎块度的关系,计算出异位孔连续装药结构岩石爆破破碎块度的分维区间,与其设计孔爆破破碎块度分维区间进行对比分析,对异位孔爆破破碎块度分维区间进行优化,利用工程实测方法与分形理论相结合找到最佳的爆破参数,以达到不规则作业面最佳爆破效果.     

带Robin边界条件的拟线性抛物方程解的整体存在性与爆破

主要研究了一类带Robin边界条件的拟线性抛物方程解的整体存在性与爆破问题,利用微分不等式技术,获得了方程的解发生爆破时的爆破时间的下界.然后给出了方程解整体存在的充分条件,最后得到了方程的解发生爆破时发生爆破时间的上界.     

一类反应扩散系统的不同时爆破临界指标(英文)

本文讨论了一类反应扩散方程组齐次第一初边值问题u_t=△u+u~mv~p,v_t=△v+u~qv~n的不同时爆破临界指标问题.在一定初值条件下,本文给出了径向解的四种同时、不同时爆破现象:存在初值使得同时爆破或不同时爆破发生;任何爆破均是同时或不同时的.通过对指标参数的完整分类给出了四种爆破现象的充分必要条件,并且得到了解的全部爆破速率估计.所得结果推广了以前的相应工作.     

非局部反应扩散方程的一致爆破速率

该文研究了带有非局部源的扩散方程的爆破速率．关于这类方程,作者证得该类方程的解整体爆破且其爆破速率在区域的任一紧子区域内是一致的．在各种情形下,当t趋向于爆破时刻T*时,|u(t)|∞的爆破速率可精确确定．     

带有非线性局部化反应源项的抛物型方程组解的一致爆破模式与边界层

考虑带有齐次Dirichlet边界条件, 反应项为非线性局部化源项的半线性抛物型方程组解的爆破性质. 首先给出了该问题的古典解在有限时刻爆破的充分条件, 以及解的两个分量同时爆破的必要条件和一个充分条件, 然后得到了解的内部一致爆破模式, 最后描述了爆破解在边界层上的渐近行为.     

一类具有对数非线性项的四阶薄膜方程新的爆破结果

该文侧重研究一类具有对数非线性项的四阶薄膜方程解的爆破现象.目前,此类问题解的爆破结果来看都依赖于井的深度d.本文中,我们建立与井的深度d无关的新爆破结论且给出爆破时间的上界.     

一类耗散型Camassa-Holm方程的解的爆破

本文研究了带耗散项λuxx的Camassa-Holm方程的局部适定性和爆破现象.由Kato定理得到局部适定性的结果,证明了解的爆破机制,并且证明了当初值满足一定条件时解发生爆破,最后研究了爆破解的爆破率.     

带具有耗散梯度项的p-Laplace方程解的爆破问题

该文研究具有耗散梯度项的一类p-Laplace方程的爆破现象.借助于合适定义的辅助函数和由此产生的一阶微分不等式,分别给出了方程的解爆破与不爆破的条件.另外,当方程的解发生爆破时,还给出了爆破时间的下界估计.     

一类多重耦合变指数抛物方程组的爆破解研究（英文）

在本文中,我们考虑一类具有非标准增长条件的多重耦合热传导方程组的齐次第一初边值问题.首先,我们研究古典解的存在唯一性,其次,我们讨论了解的爆破指标和解的整体存在性质,进一步,我们区分解的同时与不同时爆破现象,有趣的是变指数不仅仅可以区分解的爆破和整体存在而且可以区分解的同时与不同时爆破,最后,对于同时爆破的情形,在对系数和指数做一些合理假设下,我们得到解在区域上每个点都发生爆破的现象.     

GLOBAL BLOW-UP FOR A LOCALIZED DEGENERATE AND SINGULAR PARABOLIC EQUATION WITH WEIGHTED NONLOCAL BOUNDARY CONDITIONS

This paper deals with the blow-up properties of positive solutions to a localized degenerate and singular parabolic equation with weighted nonlocal boundary conditions. Under appropriate hypotheses, the global existence and finite time blow-up of positive solutions are obtained. Furthermore, the global blow-up behavior and the uniform blow-up profile of blow-up solutions are also described. We find that the blow-up set is the whole domain [0, a], including the boundaries, and this differs from parabolic equations with local sources case or with homogeneous Dirichlet boundary conditions case.     

A degenerate parabolic system with localized sources and nonlocal boundary condition

This paper deals with the blow-up properties of the positive solutions to a degenerate parabolic system with localized sources and nonlocal boundary conditions. We investigate the influence of the reaction terms, the weight functions, local terms and localized source on the blow-up properties. We will show that the weight functions play the substantial roles in determining whether the solutions will blow-up or not, and obtain the blow-up conditions and its blow-up rate estimate.     

Blow-up solutions and global solutions for nonlinear parabolic problems

This paper deals with the blow-up of positive solutions for a nonlinear parabolic equation subject to nonlinear boundary conditions. We obtain the conditions under which the solutions may exist globally or blow up in a finite time, by a new approach. Moreover, upper estimates of the “blow-up time”, blow-up rate and global solutions are obtained also.     

Blow-up solutions and global solutions for nonlinear parabolic problems

This paper deals with the blow-up of positive solutions for a nonlinear parabolic equation subject to nonlinear boundary conditions. We obtain the conditions under which the solutions may exist globally or blow up in a finite time, by a new approach. Moreover, upper estimates of the “blow-up time”, blow-up rate and global solutions are obtained also.     

A Quasilinear Parabolic System with Nonlocal Boundary Conditions and Localized Sources

This paper investigates the properties of solutions to a quasilinear parabolic system with nonlocal boundary conditions and localized sources. Conditions for the existence of global or blow-up solutions are given. Global blow-up property and blow-up rate estimates are also derived.     

Blow-up and global solutions for nonlinear reaction-diffusion equations with nonlinear boundary condition

This paper deals with the blow-up of positive solutions for a nonlinear reaction-diffusion equation subject to nonlinear boundary conditions. We obtain the conditions under which the solutions may exist globally or blow up in finite time. Moreover, an upper bound of the blow-up time, an upper estimate of the blow-up rate, and an upper estimate of the global solutions are given. At last we give two examples to which the theorems obtained in the paper may be applied.     

Non-simultaneous blow-up in localized reaction–diffusion equations

This article deals with blow-up solutions in reaction–diffusion equations coupled via localized exponential sources, subject to null Dirichlet conditions. The optimal and complete classification is obtained for simultaneous and non-simultaneous blow-up solutions. Moreover, blow-up rates and blow-up sets are also discussed. It is interesting that, in some exponent regions, blow-up phenomena depend sensitively on the choosing of initial data, and the localized nonlinearities play important roles in the blow-up properties of solutions.     

Uniform Blow-up Behavior for Degenerate and Singular Parab olic Equations

This paper deals with the degenerate and singular parabolic equations coupled via nonlinear nonlocal reactions, subject to zero-Dirichlet boundary conditions. After giving the existence and uniqueness of local classical nonnegative solutions, we show critical blow-up exponents for the solutions of the system. Moreover, uniform blow-up behaviors near the blow-up time are obtained for simultaneous blow-up solutions, divided into four subcases.     

Global solutions and blow-up problems for a nonlinear degenerate parabolic system coupled via nonlocal sources

This paper concerns with a nonlinear degenerate parabolic system coupled via nonlocal sources, subjecting to homogeneous Dirichlet boundary condition. The main aim of this paper is to study conditions on the global existence and/or blow-up in finite time of solutions, and give the estimates of blow-up rates of blow-up solutions.     

Properties of non-simultaneous blow-up solutions in nonlocal parabolic equations

This paper deals with blow-up solutions in parabolic equations coupled via nonlocal nonlinearities, subject to homogeneous Dirichlet conditions. Firstly, some criteria on non-simultaneous and simultaneous blow-up are given, including four kinds of phenomena: (i) the existence of non-simultaneous blow-up; (ii) the coexistence of non-simultaneous and simultaneous blow-up; (iii) any blow-up must be simultaneous; (iv) any blow-up must be non-simultaneous. Next, total versus single point blow-up are classified completely. Moreover, blow-up rates are obtained for both non-simultaneous and simultaneous blow-up solutions.