共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
Xu Runzhang 《Mathematical Methods in the Applied Sciences》2010,33(7):831-844
We study the Cauchy problem of nonlinear Klein–Gordon equation with dissipative term. By introducing a family of potential wells, we derive the invariant sets and prove the global existence, finite time blow up as well as the asymptotic behaviour of solutions. In particular, we show a sharp condition for global existence and finite time blow up of solutions. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
3.
4.
A parallel finite volume scheme preserving positivity for diffusion equation on distorted meshes 下载免费PDF全文
Zhiqiang Sheng Jingyan Yue Guangwei Yuan 《Numerical Methods for Partial Differential Equations》2017,33(6):2159-2178
Parallel domain decomposition methods are natural and efficient for solving the implicity schemes of diffusion equations on massive parallel computer systems. A finite volume scheme preserving positivity is essential for getting accurate numerical solutions of diffusion equations and ensuring the numerical solutions with physical meaning. We call their combination as a parallel finite volume scheme preserving positivity, and construct such a scheme for diffusion equation on distorted meshes. The basic procedure of constructing the parallel finite volume scheme is based on the domain decomposition method with the prediction‐correction technique at the interface of subdomains: First, we predict the values on each inner interface of subdomains partitioned by the domain decomposition. Second, we compute the values in each subdomain using a finite volume scheme preserving positivity. Third, we correct the values on each inner interface using the finite volume scheme preserving positivity. The resulting scheme has intrinsic parallelism, and needs only local communication among neighboring processors. Numerical results are presented to show the performance of our schemes, such as accuracy, stability, positivity, and parallel speedup.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2159–2178, 2017 相似文献
5.
Global positivity estimates and Harnack inequalities for the fast diffusion equation 总被引:1,自引:0,他引:1
We investigate local and global properties of positive solutions to the fast diffusion equation ut=Δum in the range (d−2)+/d<m<1, corresponding to general nonnegative initial data. For the Cauchy problem posed in the whole Euclidean space we prove sharp local positivity estimates (weak Harnack inequalities) and elliptic Harnack inequalities; we use them to derive sharp global positivity estimates and a global Harnack principle. For the mixed initial and boundary value problem posed in a bounded domain of with homogeneous Dirichlet condition, we prove weak and elliptic Harnack inequalities. Our work shows that these fast diffusion flows have regularity properties comparable and in some senses better than the linear heat flow. 相似文献
6.
7.
8.
9.
Olof J Staffans 《Journal of Differential Equations》1977,24(3):365-382
We consider the asymptotic behavior of the bounded solutions of a nonlinear Volterra integrodifferential equation with a positive definite convolution kernel. Our main result states that (under appropriate assumptions) the asymptotic spectra of the solutions are contained in the set where the real part of the Fourier transform of the kernel vanishes. We also give a new asymptotic stability theorem, and present a new proof of a known result on the asymptotic behavior of the bounded solutions of a nonlinear, nondifferentiated Volterra equation. 相似文献
10.
Hong Gu 《Mathematical Methods in the Applied Sciences》2016,39(3):344-352
We consider the Fisher–KPP equation with advection: ut=uxx?βux+f(u) on the half‐line x∈(0,∞), with no‐flux boundary condition ux?βu = 0 at x = 0. We study the influence of the advection coefficient ?β on the long time behavior of the solutions. We show that for any compactly supported, nonnegative initial data, (i) when β∈(0,c0), the solution converges locally uniformly to a strictly increasing positive stationary solution, (ii) when β∈[c0,∞), the solution converges locally uniformly to 0, here c0 is the minimal speed of the traveling waves of the classical Fisher–KPP equation. Moreover, (i) when β > 0, the asymptotic positions of the level sets on the right side of the solution are (β + c0)t + o(t), and (ii) when β≥c0, the asymptotic positions of the level sets on the left side are (β ? c0)t + o(t). Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
11.
Ibtissem Damergi 《Journal of Mathematical Analysis and Applications》2009,352(1):336-344
In this article we investigate the possibility of finite time blow-up in H1(R2) for solutions to critical and supercritical nonlinear Schrödinger equations with an oscillating nonlinearity. We prove that despite the oscillations some solutions blow up in finite time. Conversely, we observe that for a given initial data oscillations can extend the local existence time of the corresponding solution. 相似文献
12.
13.
K. Beauchard E. Zuazua 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009,26(5):1793-1815
In this article, we prove the null controllability of the 2D Kolmogorov equation both in the whole space and in the square. The control is a source term in the right-hand side of the equation, located on a subdomain, that acts linearly on the state. In the first case, it is the complementary of a strip with axis x and in the second one, it is a strip with axis x.The proof relies on two ingredients. The first one is an explicit decay rate for the Fourier components of the solution in the free system. The second one is an explicit bound for the cost of the null controllability of the heat equation with potential that the Fourier components solve. This bound is derived by means of a new Carleman inequality. 相似文献
14.
讨论了带有热源项的非线性扩散方程.通过一种直接简洁的方法得到了几种精确解.该方法可用于更高阶演化方程的求解问题. 相似文献
15.
Consider the renewal equation in the form (1) , where is a probability density on [0, ∞) and limt → ∞g(t) = g0. Asymptotic solutions of (1) are given in the case when f(t) has no expectation, i.e., . These results complement the classical theorem of Feller under the assumption that f(t) possesses finite expectation. 相似文献
16.
Bin Qian 《数学学报(英文版)》2011,27(6):1071-1078
Let (M,g) be a complete noncompact Riemannian manifold. In this note, we derive a local Hamilton-type gradient estimate for positive
solution to a simple nonlinear parabolic equation
$
\partial _t u = \Delta u + au\log u + qu
$
\partial _t u = \Delta u + au\log u + qu
相似文献
17.
18.
Hristo V. Kojouharov Benito M. Chen 《Numerical Methods for Partial Differential Equations》1999,15(6):617-624
A new nonstandard Eulerian‐Lagrangian method is constructed for the one‐dimensional, transient convective‐dispersive transport equation with nonlinear reaction terms. An “exact” difference scheme is applied to the convection‐reaction part of the equation to produce a semi‐discrete approximation with zero local truncation errors with respect to time. The spatial derivatives involved in the remaining dispersion term are then approximated using standard numerical methods. This approach leads to significant, qualitative improvements in the behavior of the numerical solution. It suppresses the numerical instabilities that arise from the incorrect modeling of derivatives and nonlinear reaction terms. Numerical experiments demonstrate the scheme's ability to model convection‐dominated, reactive transport problems. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 617–624, 1999 相似文献
19.
We prove an existence theorem for a nonlinear integral equation being a Volterra counterpart of an integral equation arising in the traffic theory. The method used in the proof allows us to obtain additional characterization in terms of asymptotic stability of solutions of an equation in question. 相似文献
20.
Chen Huang 《Journal of Mathematical Analysis and Applications》2022,505(2):125496
This paper considers the following general form of quasilinear elliptic equation with a small perturbation: where is a bounded domain with smooth boundary and small enough. We assume the main term in the equation to have a mountain pass structure but do not suppose any conditions for the perturbation term . Then we prove the equation possesses a positive solution, a negative solution and a sign-changing solution. Moreover, we are able to obtain the asymptotic behavior of these solutions as . 相似文献
|