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本文研究一类带奇异项的一性抛物方程的初边值问题,得到了古典解的熄灭现象,并对熄灭解的渐近行为作了分析,包含了(2-5)的相应结论。 相似文献
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《数学的实践与认识》2017,(18)
通过比较原理,讨论了有限图上带有变指数q(x)0吸收项的热方程解的熄灭和正性.当q(x)1时,证明了方程的解在有限时间熄灭,若存在图上的一个内部顶点x_0,有q(x_0)≥1,则方程的解保持严格的正性. 相似文献
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主要利用Hardy不等式及Soblev嵌入定理讨论了具奇性系数的P-Laplace方程解的熄灭性质. 相似文献
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本文研究一类带奇异项的拟线性抛物方程的初边值问题.得到了古典解的熄灭现象,并对熄灭解的渐近行为作了分析,包含了[2-5]的相应结论 相似文献
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具强吸引项的非线性反应扩散方程的解的全局熄灭问题 总被引:2,自引:0,他引:2
设f定义在[0,+∞)上的非负值连续凹函数并满足.本文证明了对于这类函数f而言,反应扩散方程ut=△u-f(u)的初值问题和具有齐次边值条件的初边值问题的解将在有限时刻全局熄灭,并给出了全局熄灭的时间估计. 相似文献
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本文在环形域上证明了带有奇异性的半线性椭圆方程边值问题(1)、(2·)在C~2(Ω)∩C~0(Ω)中正解的存在性,且这个解是径向对称的,解关于R_0(R_1)的连续单调性.还给出了解有熄灭现象的充分必要条件. 相似文献
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在Rn有界域上考虑一类带有非线性迁移项的平均曲率型方程div{σ(| Δu|2) Δu}+b(u)· Δu=0的第一类初边值问题.主要得到了弱解的存在性,并且给出了解的熄灭性质及解的L∞估计. 相似文献
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关于猝灭问题的一些结果及其应用 总被引:2,自引:0,他引:2
本文研究一类含奇异项的半线性抛物方程的初边值问题,给出了该问题的古典解整体存在或发生猝灭现象的判据以及猝灭解的生命跨度估计。同时,还用上述结果研究了一类含超Sobolev临界指标的半线性椭圆方程的Dirichlet边值问题,获得了正解的存在性结果。 相似文献
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This paper is concerned with the quenching problem of a degenerate functional reaction-diffusion equation. The quenching problem and global existence of solution for the reaction-diffusion equation are derived and, some results of the positive steady state solutions for functional elliptic boundary value are also presented. 相似文献
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《数学物理学报(B辑英文版)》2003,23(3):361-368
This paper discusses the global existence and quenching of the solution to the Newton filtration equation with the nonlinear boundary condition. The authors also discuss the profile of the quenching solution in the quenching time and obtain the quenching rate of the quenching solution. 相似文献
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This paper discusses the global existence and quenching of the solution tothe Newton filtration equation with the nonlinear boundary condition. The authors alsodiscuss the profile of the quenching solution in the quenching time and obtain the quenchingrate of the quenching solution. 相似文献
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Qiu Yi DAI Li Hui PENG 《数学学报(英文版)》2006,22(2):485-496
Let Ω be a bounded or unbounded domain in R^n. The initial-boundary value problem for the porous medium and plasma equation with singular terms is considered in this paper. Criteria for the appearance of quenching phenomenon and the existence of global classical solution to the above problem are established. Also, the life span of the quenching solution is estimated or evaluated for some domains. 相似文献
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In this paper,the initial boundary value problem of semilinear degenerate reaction-diffusion systems is studied.The regularization method and upper and lower solutions technique are employed to show the existence and continuation of a positive classical solution.The location of quenching points is found.The critical length is estimated by the eigenvalue method. 相似文献
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Quenching Time Estimates for Semilinear Parabolic Equations Controlled by Two Absorption Sources in Control System
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This paper deals with the quenching solution of the initial boundary
value problem for aclass of semilinear reaction-diffusion equation
controlled by two absorption sources in control system and estimate
upper bound and lower bound of the
quenching time. We point that the number of absorption sources
influences the time
of quenching phenomenon.The solution can solve some boundary value
problem in
control system. 相似文献
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We consider a singular reaction–diffusion system arising in modelling prey–predator interactions in a fragile environment. Since the underlying ODEs system exhibits a complex dynamics including possible finite time quenching, one first provides a suitable notion of global travelling wave weak solution. Then our study focusses on the existence of travelling waves solutions for predator invasion in such environments. We devise a regularized problem to prove the existence of travelling wave solutions for predator invasion followed by a possible co-extinction tail for both species. Under suitable assumptions on the diffusion coefficients and on species growth rates we show that travelling wave solutions are actually positive on a half line and identically zero elsewhere, such a property arising for every admissible wave speeds. 相似文献
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ABSTRACT This paper deals with blow-up and quenching solutions of degenerate parabolic problem involving m-Laplacian operator and nonlinear boundary flux. The blow-up and quenching criteria are classified under the conditions on the initial data but with less conditions on the relationship among the exponents, respectively. Moreover, asymptotic properties including singular rates, set and time estimates are determined for the blow-up solutions and the quenching solutions, respectively. 相似文献
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We prove the existence of weak global solutions to the degenerate diffusion equation (1) with singular absorption term. Moreover we investigate the regularity up to the quenching time and we show by means of explicit solutions that our regularity results are optimal. 相似文献