具强非线性耦合源的退化抛物方程组的Cauchy问题

删除或更新信息，请邮件至freekaoyan#163.com(#换成@)

本站小编 Free考研考试/2021-12-27

具强非线性耦合源的退化抛物方程组的Cauchy问题杜美华青岛理工大学琴岛学院基础部, 青岛 266106 Cauchy Problem for Degenerate Parabolic System with Strongly Nonlinear Sources DU MeihuaDepartment of Basic Courses, Qingdao University of Technology, Qindao College, Qingdao 266106, China

摘要
图/表
参考文献
相关文章(1)
点击分布统计
下载分布统计
-->

全文: PDF(323 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要本文研究了一类具强非线性耦合源的退化抛物方程组的Cauchy问题，其中初值为Radon测度.我们得到的主要结果有两个：首先，利用先验估计和方程组的结构，我们克服了方程组主部的退化性与强非线性耦合源相互作用带来的困难，对该问题得到了解的存在性；其次，通过选取恰当的检验函数，我们证明了测度初值解的存在性在所考虑的类中是最优的.本文所得到的结果改进了已有的研究结果.

服务

加入引用管理器

E-mail Alert

RSS

收稿日期: 2019-12-10

PACS:

O175.2

基金资助:国家自然科学基金（11201124）资助项目.

引用本文:

杜美华. 具强非线性耦合源的退化抛物方程组的Cauchy问题[J]. 应用数学学报, 2020, 43(6): 939-948. DU Meihua. Cauchy Problem for Degenerate Parabolic System with Strongly Nonlinear Sources. Acta Mathematicae Applicatae Sinica, 2020, 43(6): 939-948.

链接本文:

http://123.57.41.99/jweb_yysxxb/CN/或 http://123.57.41.99/jweb_yysxxb/CN/Y2020/V43/I6/939

[1]	Andreucci D. New results on the Cauchy problem for parabolic systems and equations with strongly nonlinear sources. Manuscripta Math., 1992, 77:127-159
[2]	Andreucci D, Herrero M A, Velázquez J J L. Liouville theorems and blow up behavior in semilinear reaction-diffusion systems. Ann. Inst. H. Poincaré Anal. Non Linéaire, 1997, 14:1-53
[3]	Chen H W. Global existence and blow-up for a nonlinear reaction-diffusion system. J. Math. Anal. Appl., 1997, 212:481-492
[4]	Escobedo M, Levine H A. Explosion et existence globale pour un systéme faiblement couplé d'équations de réaction diffusion. C. R. Acad. Sci. Paris Sér. I, 1992, 314:735-739
[5]	Escobedo M, Levine H A. Critical blowup and global existence numbers for a weakly coupled system of reaction-diffusion equations. Arch. Ration. Mech. Anal., 1995, 129:47-100
[6]	Wang M X. Global existence and finite time blow up for a reaction-diffusion system. Z. Angew. Math. Phys., 2000, 51:160-172
[7]	Chen C S. Global existence and estimates of solutions for a quasilinear parabolic system. J. Evol. Equ., 2006, 6:29-43
[8]	Shang H F, Deng L H. Local and global existence for quasilinear parabolic systems with a strongly nonlinear source. Nonlinear Anal., 2012, 75:4014-4024
[9]	Andreucci D, DiBenedetto E. On the Cauchy problem and initial traces for a class of evolution equations with strongly nonlinear sources. Ann. Scuola Norm. Sup. Pisa Cl. Sci. Ser. 4, 1991, 18(3):393-441
[10]	Zhao J N. On the Cauchy problem and initial traces for the evolution p-Laplacian equations with strongly nonlinear sources. J. Differential Equations, 1995, 121:329-383
[11]	Chen M Y, Zhao J N. On the Cauchy problem of evolution p-Laplacian equation with nonlinear gradient term. Chin. Ann. Math., 2009, 30(1):1-16
[12]	Shang H F, Li F Q. On the Cauchy problem for the evolution p-Laplacian equations with gradient term and source and measures as initial data. Nonlinear Anal., 2010, 72:3396-3411
[13]	Zhao J N, Lei P D. On the Cauchy problem of evolution p-Laplacian equations with strongly nonlinear sources when 1 Acta Math. Sin. (Engl. Ser.), 2001, 17(3):455-470
[14]	Lian S Z, Yuan H J, Cao C L, Gao W J, Xu X J. On the Cauchy problem for the evolution p-Laplacian equations with gradient term and source. J. Differential Equations, 2007, 235:544-585
[15]	Shang H F. Local and global existence for evolution p-Laplacian equation with time-dependent source. Appl. Anal., 2013, 92(3):562-572
[16]	Andreucci D. Degenerate parabolic equations with initial data measures. Trans. Amer. Math. Soc., 1997, 349(10):3911-3923
[17]	Ladyzhenskaja O A, Solonikov V A, Ural'ceva N N. Linear and quasilinear equations of parabolic type. Amer. Math. Soc., Providence:RI, 1968
[18]	Lions J L. Quelques méthodes de résolution des problémes aux limites nonlinéaires. Dunod:Paris, 1969
[19]	Chen Y Z, DiBenedetto E. Boundary estimates for solutions of nonlinear degenerate parabolic systems. J. Reine Angew. Math., 1989, 395:102-131
[20]	DiBenedetto E. Degenerate Parabolic Equations. New York:Springer-Verlag:1993
[21]	伍卓群, 赵俊宁, 尹景学, 李辉来. 非线性扩散方程. 吉林:吉林大学出版社, 2001 (Wu Z Q, Zhao J N, Yin J X, Li H L. Nonlinear diffusion equations. Jilin:Jilin University Press, 2001)

[1]	王元, 徐广善, 杨照华. 数理方程近似求解的数论方法[J]. 应用数学学报(英文版), 1999, 22(4): 541-547.

PDF全文下载地址:

http://123.57.41.99/jweb_yysxxb/CN/article/downloadArticleFile.do?attachType=PDF&id=14830