一类双重退化抛物型方程的Cauchy问题

Cauchy Problems for a Class of Doublely Degenerate Parabolic Equations

LING Zhengqiu¹,², WANG Zejia³,⁴

1. Institute of Mathematics, Jilin University, Changchun 130012, China; 2. Department of Mathematics and Computer Science, Yulin Normal University, Yulin 537000, Guangxi Zhuang Autonomous Region, China;3. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China;4. College of Mathematics, Jilin University, Changchun 130012, China

Received:2005-12-30 Revised:1900-01-01 Online:2006-09-26 Published:2006-09-26
Contact: WANG Zejia

Abstract

Abstract: This paper is concerned with the Cauchy problem for a class of degenerate parabolic equations, which describes the movement of liquid in porous media, i.e., filtration. The definitions of the entropy solution and the weak solution were proposed, then by virtue of the regularized problem, the existence of the entropy solution was shown by using the compensatory compact theorem. Furthermore, the stability of the entropy solution was obtained by the double variable method.

Key words: doublely degenerate parabolic equation, entropy solution, stability

CLC Number:

O175.8

LING Zhengqiu,, WANG Zejia,. Cauchy Problems for a Class of Doublely Degenerate Parabolic Equations[J].J4, 2006, 44(05): 679-686.

[1]	JIN Manli, LIN Yuguo. tationary Distribution of Stochastic SIREpidemic Model and Its Stability [J]. Journal of Jilin University Science Edition, 2017, 55(06): 1379-1386.
[2]	LIU Juan, ZHANG Xin. Stability of a Class of Delayed SIQR Epidemic Models [J]. Journal of Jilin University Science Edition, 2017, 55(06): 1477-1480.
[3]	ZHANG Lichun, HUANG Qingdao, YANG Yueting, CAI Shuyun. Local Stability of Two Periodic Positive Solutions ofa Second Order Rational Nonlinear Difference Equation [J]. Journal of Jilin University Science Edition, 2016, 54(03): 451-456.
[4]	XU Shuai, HUA Li, HOU Hanna. Hydrothermal Synthesis Magnetic Nanometer Microsphere ofNiFe₂O₄and Its Electrochemical Stability Analysis [J]. Journal of Jilin University Science Edition, 2016, 54(02): 388-390.
[5]	ZHANG Lei, YANG Yang, LIN Jie, LIU Xingyuan. Amplified Spontaneous Emission Propertiesof a BODIPY Derivative [J]. Journal of Jilin University Science Edition, 2015, 53(05): 1027-1030.
[6]	LI Yanbo, GUO Hua. Stability of Downward Continuation of BoundaryConditions of Wave Equation Inversion [J]. Journal of Jilin University Science Edition, 2014, 52(04): 743-745.
[7]	SHI Sanzhi, YAN Li, WANG Zesheng. Maximum Likelihood Estimate of TimeVaryingParameter Autoregression Model [J]. Journal of Jilin University Science Edition, 2013, 51(06): 1098-1100.
[8]	SHI Luoyi, WU Yujing. Stability of Amenable Operators [J]. Journal of Jilin University Science Edition, 2013, 51(05): 826-830.
[9]	WANG Peng, HAN Yuecai. Splitstep Backward Milstein Methods for Stiff Stochastic Systems [J]. J4, 2009, 47(6): 1150-1154.
[10]	LI Lin-Song, PIAO Jing-Song, SHU Hong-Hua. Ulam Stability of Quadratic Functional Equation inthe Space of \|Distributions [J]. J4, 2009, 47(4): 691-694.
[11]	TUN Chun-Ji, Zhang-E-Na, WANG Wen-Quan, Zhang-Jin-Bao, Su-Feng-. Effects of Addition Elements on \|Glass\\|forming Ability and Thermostability of \|Mg-Based Amorphous Alloys  [J]. J4, 2009, 47(05): 1042-1046.
[12]	LI Junling，, ZHANG Shugong. Variable Horizon Robust Model Predictive Control for Timevarying Uncertain Systems [J]. J4, 2008, 46(06): 1007-1012.
[13]	XU Xu, ZHANG Jie, LIANG Yanchun. Effects of Small World Connection on the Stability of a Neural Network [J]. J4, 2008, 46(05): 873-876.
[14]	CHEN Xumei, WANG Linjun, ZHANG Ran. Generalized Strong Practical Stability of 1-DOF Model [J]. J4, 2008, 46(05): 829-835.
[15]	WANG Peng, Lv Xianrui, ZHANG Shen xu. Threestage Semiimplicit Stochastic RungeKutta Methods for Stochastic Differential Equations [J]. J4, 2008, 46(02): 219-223.

Cauchy Problems for a Class of Doublely Degenerate Parabolic Equations

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10