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排序方式: 共有266条查询结果,搜索用时 15 毫秒
1.
In this paper we consider an initial boundary value problem for a reaction-diffusion equation under nonlinear and nonlocal Robin type boundary condition. Assuming the existence of an ordered pair of upper and lower solutions we establish a generalized quasilinearization method for the problem under consideration whose characteristic feature consists in the construction of monotone sequences converging to the unique solution within the interval of upper and lower solutions, and whose convergence rate is quadratic. Thus this method provides an efficient iteration technique that produces not only improved approximations due to the monotonicity of its iterates, but yields also a measure of the convergence rate. 相似文献
2.
Guillemette Chapuisat 《Journal of Differential Equations》2007,236(1):237-279
This paper deals with the existence of curved front solution of a partial differential equation coming from a mathematical model of stroke. The equation is of reaction-diffusion type in a cylinder of radius R and of diffusion and absorption type outside of the cylinder. We prove the nonexistence of a travelling front when R is small enough and the existence if R is large enough using a recent energy method. We construct the travelling front as the limit in time of a solution with a well-chosen initial condition, in a travelling referential. 相似文献
3.
Yuan-Ming Wang 《Journal of Mathematical Analysis and Applications》2007,328(1):137-150
The aim of this paper is to investigate the asymptotic behavior of solutions for a class of three-species predator-prey reaction-diffusion systems with time delays under homogeneous Neumann boundary condition. Some simple and easily verifiable conditions are given to the rate constants of the reaction functions to ensure the convergence of the time-dependent solution to a constant steady-state solution. The conditions for the convergence are independent of diffusion coefficients and time delays, and the conclusions are directly applicable to the corresponding parabolic-ordinary differential system and to the corresponding system without time delays. 相似文献
4.
V. Afraimovich A. Babin S.-N. Chow 《Transactions of the American Mathematical Society》1996,348(12):5031-5063
The dynamics described by a system of reaction-diffusion equations with a nonlinear potential exhibits complicated spatial patterns. These patterns emerge from preservation of homotopy classes of solutions with bounded energies. Chaotically arranged stable patterns exist because of realizability of all elements of a fundamental homotopy group of a fixed degree. This group corresponds to level sets of the potential. The estimates of homotopy complexity of attractors are obtained in terms of geometric characteristics of the potential and other data of the problem.
5.
Finite Difference Method for Reaction-Diffusion Equation with Nonlocal Boundary Conditions 总被引:2,自引:0,他引:2
Jianming Liu 《高等学校计算数学学报(英文版)》2007,16(2):97-111
In this paper, we present a numerical approach to a class of nonlinear reaction-diffusion equations with nonlocal Robin type boundary conditions by finite difference methods. A second-order accurate difference scheme is derived by the method of reduction of order. Moreover, we prove that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete L2-norm. A simple numerical example is given to illustrate the efficiency of the proposed method. 相似文献
6.
7.
本文考虑了一类带有多项式非线性项的高维反应扩散方程.建立了一个全离散的有限差分格式,并证明了差分解的存在唯一性.分析了由差分格式生成的离散系统的动力性质,在对差分解先验估计的基础上得到了离散动力系统的整体吸引子的存在性.最后证明了差分格式的长时间稳定性和收敛性. 相似文献
8.
研究含时滞反应扩散Giu-Lawson方程的行波解.利用波前解的存在性理论,通过构造一个二阶时滞微分方程的上解和下解,得到当时滞较小时,微分方程的波前解存在,当时滞较大时,即使微分方程的行波解存在,也必将失去单调性的结论. 相似文献
9.
61.Intr0ducti0nInthispaper,wediscussareactionnetinacombusti0nmodel:V={R,,R2},whereR,andR2aredistinctreacti0nprocesses:Rl:A1+A,-A,,R2:A2+A3-P,A,(j=1,2,3)denotesthereactant,andPdenotestheinertproduct.Thesereactionsareexothermicreactions-LetQ,,Q2standforheatenergiesandU=(U,,U,,U,,U,)forstatevariablesdescribingreactions,whereUoisreactiontemporature,andU,(j=1,2,3)isthemolarityofthej-threactant.AssumethatV,(i=1,2)isthereactantvariablefortheithreactionpr0cess:V,=(Q,,1,-l,l)",V2=(Q,,O,-l,-… 相似文献
10.
Bieniasz LK 《Computational Biology and Chemistry》2003,27(3):315-325
Accurate calculation of concentration gradients at the boundaries is crucial in electrochemical kinetic simulations, owing to the frequent occurrence of gradient-dependent boundary conditions, and the importance of the gradient-dependent electric current. By using the information about higher spatial derivatives of the concentrations, contained in the time-dependent, kinetic reaction-diffusion partial differential equation(s) in one-dimensional space geometry, under appropriate assumptions it is possible to increase the accuracy orders of the conventional, one-sided n-point finite-difference formulae for the concentration gradients at the boundaries, without increasing n. In this way a new class of high order accurate gradient approximations is derived, and tested in simulations of potential-step chronoamperometric and current-step chronopotentiometric transients for the Reinert-Berg system. The new formulae possess advantages over the conventional gradient approximations. For example, they allow one to obtain a third order accuracy by using two space points only, or fourth order accuracy by using three points, and yet they yield smaller errors than the conventional four-point, or five-point formulae, respectively. Needing fewer points, for approximating the gradients with a given accuracy, simplifies also the solution of the linear algebraic equations arising from the application of implicit time integration schemes. 相似文献