两个拟线性退化抛物型方程柯西问题弱解存在性的同一种求解方法  

On Same Solution to Existence of Weak Solution for Cauchy Problem of Two Quasilinear Degenerate Parabolic Equations

作　　者：旷雨阳 黄宝勤 赵彩霞 KUANG Yu-yang;HUANG Bao-qin;ZHAO Cai-xia(College of mathematics and physics,Anshun University,Anshun Guizhou 56100,China)

机构地区：[1]安顺学院数理学院,贵州安顺561000

出　　处：《西南师范大学学报（自然科学版）》2018年第7期1-7,共7页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：贵州省科学技术厅;安顺市人民政府;安顺学院三方联合基金项目(黔科合LH字[2017]7050号)

摘　　要：先构造一个压缩算子半群,后用此压缩算子半群分别去求解如下两个齐次与非齐次的拟线性退化抛物型方程的柯西问题的弱解存在性:{?u/?t-ΔΦ(u)=0(x,t)∈R^n×R^+ u(x,0)=u_0(x)x∈R ~n{?u/?t-ΔΦ(u)=f(x,t)(x,t)∈R^n×R^+ u(x,0)=0 x∈R^n其中:Δ为拉普拉斯算子,Φ(s)∈C^2(R),Φ(0)=0,Φ′(s)≥0,且集合{s∈R|Φ′(s)=0}不含有内点.In this paper,a compact semigroup of operators is firstly constructed,and then the semigroup of compact operators used to solve the existence of the weak solutions of the Cauchy problem for two homogeneous and nonhomogeneous Quasilinear Degenerate Parabolic equations：{？u/？t-ΔΦ（u）=0（x,t）∈R^n×R~＋ u（x,0）=u_0（x）x∈R ~n and {？u/？t-ΔΦ（u）=f（x,t）（x,t）∈R^n×R~＋ u（x,0）=0 x∈R^nAmongΔis laplasse operator,Φ（s）∈C^2（R）,Φ（0）=0,Φ′（s）≥0,and aggregate{s∈R｜Φ′（s）=0}does not contain internal points.

关 键 词：拟线性退化抛物型方程 柯西问题 弱解 算子半群理论 

分 类 号：O175.26[理学—数学]