一类抛物型方程弱解的正则性  

Regularity of the weak solutions for a class of parabolic equation

作　　者：狄华斐[1] 武虔虔[1] 龙群飞[1] 

机构地区：[1]云南民族大学数学与计算机科学学院

出　　处：《贵州师范大学学报（自然科学版）》2012年第2期28-32,共5页Journal of Guizhou Normal University：Natural Sciences

基　　金：国家自然科学基金(批准号:10861014)

摘　　要：对一类PDE抛物型方程初边值问题,在一定条件假设下弱解的正则性问题的研究,通过一些技巧和方法,描述了方程弱解的正则性.这些技巧和方法包括:Galerkin逼近法,解得弱收敛,sobolev不等式,内插不等式等等.In this paper, we discuss the regularity of the weak solution u to the initial/boundary value problem for second-order parabolic equations under certain Condition assumption. Via some techniques and methods, we also show the regularity of the weak solution. These techniques and methods include Galinkin-approximation, the weak convergence of the solutions, Sobolev-inequalities, interpolation-inequality, etc.

关 键 词：抛物型方程 弱解 弱解的正则性 GALERKIN逼近 

分 类 号：O29[理学—应用数学]