WELL-POSEDNESS OF WEAK SOLUTIONS TO ELECTRORHEOLOGICAL FLUID EQUATIONS WITH DEGENERACY ON THE BOUNDARY

被引：0

作者：

Zhan, Huashui ^{[1
]}

Wen, Jie ^{[2
]}

机构：

[1] Xiamen Univ Technol, Sch Appl Math, Xiamen 361024, Fujian, Peoples R China

[2] Jimei Univ, Sch Sci, Xiamen 361021, Fujian, Peoples R China

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年

关键词：

Electrorheological fluid equation; boundary degeneracy; Holder's inequality; local stability; EXISTENCE;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article we study the electrorheological fluid equation ut = div(rho(alpha)vertical bar del u vertical bar(p(x)-2)del v), where rho(x) = dist(x, partial derivative Omega) is the distance from the boundary, p(x) is an element of C-1 ((Omega) over bar), and p(-) = min(x is an element of(Omega) over bar)p(x) > 1 We show how the degeneracy of rho(alpha) on the boundary affects the well-posedness of the weak solutions. In particular, the local stability of the weak solutions is established without any boundary value condition.

引用

页数：15

共 17 条

[11]

Ruzicka M, 2000, LECT NOTES MATH, V1748, P1

[12]

Taylor Michael E., 1999, APPL MATH SCI

[13] Holder regularity for the general parabolic p(x, t)-Laplacian equations [J].

Yao, Fengping .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2015, 22 (01) :105-119

[14] Properties of the boundary flux of a singular diffusion process [J].

Yin, JX ;

Wang, CP .

CHINESE ANNALS OF MATHEMATICS SERIES B, 2004, 25 (02) :175-182

[15]

Zhan HS, 2015, BOUND VALUE PROBL, DOI 10.1186/s13661-015-0377-6

[16] Global gradient estimates for the parabolic p(x, t)-Laplacian equation [J].

Zhang, Chao ;

Zhou, Shulin ;

Xue, Xiaoping .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 105 :86-101

[17]

Zhikov VV., 2004, ZAP NAUCHN SEM S PET, V310, P67

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