共查询到20条相似文献,搜索用时 31 毫秒
1.
L.E. Payne 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(4):971-1014
This paper deals with the blow-up of the solution to a semilinear second-order parabolic equation with nonlinear boundary conditions. It is shown that under certain conditions on the nonlinearities and data, blow-up will occur at some finite time and when blow-up does occur upper and lower bounds for the blow-up time are obtained. 相似文献
2.
Fei Liang 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):2189-2198
This paper deals with the blow-up for a system of semilinear r-Laplace heat equations with nonlinear boundary flux. It is shown that, under certain conditions on the nonlinearities and data, blow-up will occur at some finite time, and when blow-up does occur upper and lower bounds for the blow-up time are obtained. 相似文献
3.
Cristian Enache 《Applied Mathematics Letters》2011,24(3):288-292
This note deals with a class of heat emission processes in a medium with a non-negative source, a nonlinear decreasing thermal conductivity and a linear radiation (Robin) boundary condition. For such heat emission problems, we make use of a first-order differential inequality technique to establish conditions on the data sufficient to guarantee that the blow-up of the solutions does occur or does not occur. In addition, the same technique is used to determine a lower bound for the blow-up time when blow-up occurs. 相似文献
4.
研究了非线性抛物方程在非线性边界条件下的解的爆破问题,通过构造一个能量表达式,运用微分不等式的方法,得到该能量表达式所满足的微分不等式,然后通过积分得到当爆破发生时解在非线性边界条件下的爆破时间的下界. 相似文献
5.
本文考虑非线性边界条件的反应扩散方程组的爆破速率。在某种假设下给出了爆破的精确速率,同时证明了爆破不在区域的内部发生。 相似文献
6.
Gongwei Liu & Shuying Tian 《分析论及其应用》2022,38(4):451-466
We investigate the initial boundary value problem of some semilinear pseudo-parabolic equations with Newtonian nonlocal term. We establish a lower bound for the blow-up time if blow-up does occur. Also both the upper bound for $T$ and blow up rate of the solution are given when $J(u_0)<0$. Moreover, we establish the blow up result for arbitrary initial energy and the upper bound for $T$. As a product, we refine the lifespan when $J(u_0)<0.$ 相似文献
7.
8.
We consider the blow-up of solutions of equations of the form
by means of a differential inequality technique. A lower bound for blow-up time is determined if blow-up does occur as well as a criterion for blow-up and conditions which ensure that blow-up cannot occur. 相似文献
ut=div(ρ(|∇u|2) grad u)+f(u)
9.
本文考虑具有 Neumann边界条件 u/n=ev, v/η=eu在 SR ×(0,T)热方程组。ut=△u,vt=△v在BR×(0,T)解的爆破性质·我们给出了爆破速度估计并证明了爆破仅在边界上发生. 相似文献
10.
《应用数学年刊》2014,(4)
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. 相似文献
11.
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. 相似文献
12.
13.
针对一类具有Dirichlet边界条件的非线性反应扩散方程的爆破问题,通过构造恰当的辅助函数和利用一阶微分不等式技术,给出了解在有限时刻爆破的一个充分条件,并在一定条件下得到了爆破时刻的上界和下界. 相似文献
14.
This paper considers the finite time blow-up of nonnegative solutions for a nonlinear diffusion system with a more complicated source term, which is a product of localized source, local source, weight function, and complemented by homogeneous Dirichlet boundary conditions. It is proved that there exists initial data such that simultaneous or non-simultaneous blow-up occur. Moreover, the related classifications for the four parameters in the model is optimal and complete. The results extend those in Zhang and Yang (J. Appl. Math. Comput. 32:429?C441, 2010). 相似文献
15.
This paper deals with parabolic equations with different diffusion coefficients and coupled nonlinear sources, subject to homogeneous Dirichlet boundary conditions. We give many results about blow-up solutions, including blow-up time estimates for all of the spatial dimensions, the critical non-simultaneous blow-up exponents, uniform blow-up profiles, blow-up sets, and boundary layer with or without standard conditions on nonlocal sources. The conditions are much weaker than the ones for the corresponding results in the previous papers. 相似文献
16.
This paper considers the prescribed zero scalar curvature and mean curvature problem on the n-dimensional Euclidean ball for n?3. We consider the limits of solutions of the regularization obtained by decreasing the critical exponent. We characterize those subcritical solutions which blow-up at the least possible energy level, determining the points at which they can concentrate, and their Morse indices. We show that when n=3 this is the only blow-up which can occur for solutions. We use this in combination with the Morse inequalities for the subcritical problem to obtain a general existence theorem for the prescribed zero scalar curvature and mean curvature on the three-dimensional Euclidean ball. In the higher-dimensional case n?4, we give conditions on the function h to guarantee there is only one simple blow-up point. 相似文献
17.
E. V. Yushkov 《Differential Equations》2012,48(9):1212-1218
We use the nonlinear capacity method to prove the blow-up of solutions of initial-boundary value problems of hydrodynamic type in bounded domains. We present sufficient boundary conditions ensuring the blow-up of the solution of an equation that is globally solvable under the classical boundary conditions. We estimate the blow-up time of solutions under given initial conditions. Note that it is the first result concerning blow-up for one of the problems considered. 相似文献
18.
Zhihua Dong 《Applicable analysis》2018,97(5):825-841
This paper deals with a parabolic system with different diffusion coefficients and coupled nonlocal sources, subject to homogeneous Dirichlet boundary conditions. The conditions on global existence, simultaneous or non-simultaneous blow-up, blow-up set, uniform blow-up profiles and boundary layer are got using comparison principle and asymptotic analysis methods. 相似文献
19.
Blow-up for a semilinear reaction-diffusion system coupled in both equations and boundary conditions
Sheng-Chen FuJong-Shenq Guo 《Journal of Mathematical Analysis and Applications》2002,276(1):458-475
We study the blow-up behavior for a semilinear reaction-diffusion system coupled in both equations and boundary conditions. The main purpose is to understand how the reaction terms and the absorption terms affect the blow-up properties. We obtain a necessary and sufficient condition for blow-up, derive the upper bound and lower bound for the blow-up rate, and find the blow-up set under certain assumptions. 相似文献
20.
《Nonlinear Analysis: Theory, Methods & Applications》2009,70(12):4567-4574
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. 相似文献