一类多维反应扩散方程组初边值问题整体强解的存在唯一性  

Existence and uniqueness of global strong solutions of the initial boundary value problem for a class of systems of reaction-diffusion equations in biophysics

作　　者：徐润章[1] 

机构地区：[1]哈尔滨工程大学理学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2007年第7期832-834,共3页Journal of Harbin Engineering University

基　　金：国家自然科学基金资助项目(10271034);哈尔滨工程大学基础研究基金资助项(HEUF04012);哈尔滨工程大学创新项目(ZE01)

摘　　要：研究从生物物理学中提出的一类反应扩散方程组的初边值问题,通过对非线性项作出增长性、有界性和连续性的假设,利用近似解的积分估计和Galerkin方法证明了整体强解的存在性,并证明了解的唯一性.其结果说明了解的存在时间为0～∞,并为数值求解提供了可能性和理论基础.This paper studies the initial boundary value problem for a class of systems of reaction-diffusion equations arising in biophysics. With the assumptions of increasing property, boundedness and continuity on nonlinear terms, the existence of global strong solutions was proved using integral estimates of approximate solutions and the Galerkin method. The uniqueness of the solutions were also proved. The results indicate that the existence time of the solutions was from zero to infinite, proving their feasibility and giving a theoretical foundation for numerical solutions to this kind of problems.

关 键 词：反应扩散方程组 初边值 整体强解 存在性 唯一性 

分 类 号：O175.26[理学—数学]