一类含梯度项的奇异抛物型方程弱解的存在性  

Existence of Weak Solutions for Some Singular Parabolic Equations with Gradient Terms

作　　者：张亚茹 夏莉 ZHANG Yaru;XIA Li(School of Statistics and Mathematics,Guangdong University of Finance and Economic,Guangzhou 510320,China;Big Data and Educational Statistics Application Laboratory,Guangdong University of Finance and Economic,Guangzhou 510320,China)

机构地区：[1]广东财经大学统计与数学学院,广州510320 [2]广东财经大学大数据与教育应用统计实验室,广州510320

出　　处：《华南师范大学学报（自然科学版）》2023年第3期96-102,共7页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11971200);广东省教育厅科研项目[特色创新项目](2018KTSCX069);广东省教育厅委托项目(0835-210Z33606691)。

摘　　要：文章研究一类具有Dirichlet边界条件和初始条件的含梯度项奇异抛物型偏微分方程:{y_(t)-y″-κ/ry′+λ|y′|^(2)y^(m)=f(r,t)(y≥0,(r,t)?(0,1)×(0,T]),y(0,t)=y(1,t)=0(t?(0,T]),y(r,0)=φ(r)(r?(0,1)),其中,T>0,κ≥0,λ>0,m?(0,2)。由于含梯度的奇异抛物型方程中具有奇异项和非线性项,故先利用抛物正则化方法将方程进行正则化,再结合上下解方法,证明了在不同假设条件下的该类方程非负弱解的存在性。最后,证明了该方程的弱比较原理。A class of singular parabolic equations with gradient terms is studied in this paper,with Dirichlet boun-dary condition and initial condition,of the from {y_(t)-y″-κ/ry′+λ|y′|^(2)y^(m)=f(r,t)(y≥0,(r,t)?(0,1)×(0,T]),y(0,t)=y(1,t)=0(t?(0,T]),y(r,0)=φ(r)(r?(0,1)),where T>0,κ≥0,λ>0 and m?(0,2).Since singular parabolic equations containing gradient terms have singular terms and nonlinear terms,the parabolic regularization method is used to regularize the equation,and then combined with the sub-super solutions method,the existence of weak solutions of the equations under different assumptions is proved.Finally,the weak comparison principle of the equations is proved.

关 键 词：存在性 奇异抛物型方程 弱解 

分 类 号：O175.26[理学—数学]