«上一篇/Previous Article|本期目录/Table of Contents|下一篇/Next Article»

《集美大学学报（自然科学版）》[ISSN:1007-7405/CN:35-1186/N]

卷:

第16卷

期数:

2011年第4期

页码:

306-310

栏目:

数理科学与信息工程

出版日期:

2011-07-25

文章信息/Info

Title:

Stability of Entropy Solution to the Cauchy Problem for a Nonlinear Hyperbolic-Parabolic Equation

作者:

陈淑琴; 詹华税

(集美大学理学院,福建 厦门 361021)

Author(s):

CHEN Shu-qin; ZHAN Hua-shui

(School of Science,Jimei University,Xiamen 361021,China)

关键词:

稳定性; 熵解; 双曲-抛物方程

Keywords:

stability; entropy solutions; hyperbolic -parabolic equation

分类号:

-

DOI:

-

文献标志码:

-

摘要:

考虑抛物-双曲方程：ut+a(x,t)/2·▽u2=Δu+,t＞0,其中a是向量值函数，div a≤0，且u+=max{u,0}.该方程在[u＜0]上是双曲方程，在[u＞0]上是抛物方程.证明了若该方程的熵解在x→∞时不超过线性增长，那么它在加权的空间中解具有稳定性.同时，说明了线性增长条件对于它的解的唯一性成立时已经是最优化的条件了

Abstract:

The cauchy problem for a nonlinear hyperbolic-parabolic equation ut+a(x,t)/2·▽u2=Δu+,t＞0 was considered,where a was a variable vector,div a≤0,and u+= max{u,0}.The equation was hyperbolic equation in the region [u<0] and parabolic in the region [u>0].It was shown that entropy solution to the equation that grew at most linearly as x→∞ was stable in a weighted space,which implied that the solutions were unique.The linear growth as x→∞ imposed on the solution was shown to be optimal for uniqueness to hold

参考文献/References:

-

相似文献/References:

[1]辛云冰.缓变系数线性中立型系统的稳定性[J].集美大学学报(自然科学版),2010,15(4):308.
　XIN Yun-bing.The Stability of Slowly Varying Coefficient with theNeutral Functional Differential Equations[J].Journal of Jimei University,2010,15(4):308.
[2]陈建弘,黄龙光.Minty型含参数拟变分锥的稳定性[J].集美大学学报(自然科学版),2012,17(4):301.
　CHEN Jian-hongHUANG Long-guang.Stability of Parametric Quasivariational Cone of the Minty Type[J].Journal of Jimei University,2012,17(4):301.
[3]吴海龙,陈雪芳,王诚,等.章鱼内脏胰蛋白酶抑制剂的分离纯化与性质研究[J].集美大学学报(自然科学版),2013,18(4):246.
　WU Hai-longCHEN Xue-fang,WANG Cheng,CAI Qiu-feng,et al.Purification and Characterization of a Trypsin Inhibitor from the Viscera of Octopus(Octopus fangsiao)[J].Journal of Jimei University,2013,18(4):246.
[4]钟小容,王凤筵,张树文,等.捕食者染病的生态流行病系统的稳定性[J].集美大学学报(自然科学版),2014,19(6):459.
　ZHONG Xiao-rong,WANG Feng-yan,ZHANG Shu-wen,et al.The Stability of Eco-epidemiological Model with Infected Predator[J].Journal of Jimei University,2014,19(4):459.
[5]许文彬.p-拉普拉斯抛物型方程解的稳定性[J].集美大学学报(自然科学版),2016,21(6):471.
　XU Wen-bin.On the Stability of a Parabolic Equation Related to the p-Laplacian[J].Journal of Jimei University,2016,21(4):471.
[6]周臻,詹华税.一类非线性退化抛物方程的解[J].集美大学学报(自然科学版),2017,22(6):70.
　ZHOU Zhen,ZHAN Huashui.Solutions of a Nonlinear Degenerate Parabolic Equation[J].Journal of Jimei University,2017,22(4):70.
[7]潘冰青,刘光明,曹敏杰,等.鲤鱼胶原蛋白的过敏原性研究[J].集美大学学报(自然科学版),2011,16(5):340.
　PAN Bing-qing,LIU Guang-ming,CAO Min-jie,et al.IgEStudy on the Allergen of Collagen Isolated fromSkin of Carp(Cyprinus carpio)[J].Journal of Jimei University,2011,16(4):340.
[8]叶星旸.基于分数阶微分方程的木马病毒传播规律[J].集美大学学报(自然科学版),2019,24(2):145.
　YE Xingyang.An Epidemic Model of the Trojan Virus Propagation Based on Fractional Differential Equations[J].Journal of Jimei University,2019,24(4):145.
[9]古强,王荣杰.带恒功率负载的Boost变换器建模与稳定性分析[J].集美大学学报(自然科学版),2020,25(1):57.
　GU Qiang,WANG Rongjie.Modeling and Stability Analysis on Boost Converter Feeding Constant Power Load[J].Journal of Jimei University,2020,25(4):57.
[10]闫瑞娥,梁宗旗.具波动算子非线性Schrodinger方程线性化差分格式[J].集美大学学报(自然科学版),2020,25(2):146.
　YAN Ruie,LIANG Zongqi.Linearized Difference Scheme for Nonlinear Schrodinger Equation with Wave Operator[J].Journal of Jimei University,2020,25(4):146.

备注/Memo

备注/Memo:

-

常用功能

更新日期/Last Update: 2018-06-13