[1]徐承龙.一类重特征偏微分方程的可解性[J].东南大学学报(自然科学版),1987,17(2):126-136.[doi:10.3969/j.issn.1001-0505.1987.02.014]
 Xu Chenglong(Departmen of Mathematics and Mechanics).The Solvability for a Class of Partial Diffferential Eqnatious with Double Characteristies[J].Journal of Southeast University (Natural Science Edition),1987,17(2):126-136.[doi:10.3969/j.issn.1001-0505.1987.02.014]
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一类重特征偏微分方程的可解性()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
17
期数:
1987年第2期
页码:
126-136
栏目:
本刊信息
出版日期:
1987-03-20

文章信息/Info

Title:
The Solvability for a Class of Partial Diffferential Eqnatious with Double Characteristies
作者:
徐承龙
南京工学院数学力学系
Author(s):
Xu Chenglong(Departmen of Mathematics and Mechanics)
关键词:
偏微分方程 重特征 第二类混合问题 柯西问题 可解性
Keywords:
partial differential equation double characteristics second-mixed problem Cauchy problem solvability
分类号:
+
DOI:
10.3969/j.issn.1001-0505.1987.02.014
摘要:
本文讨论了方程■的第二类混合问题及柯西问题的可解性。证明了当c■-(b-a)(k+1)j(j-0,1,…)时,具第二类边界的混合问题有唯一的c解;当c=-(b-a)(k+1)j时,解的存在性、唯一性都失去。给出了解存在的充分必要条件,并证明一类修改问题解的存在唯一性。最后,用延拓的方法讨论了柯西问题的一可解性。
Abstract:
This paper discusses the solvability for second-mixed problem and Cauchy problem of the equation p(c)u=((?)_t+at^k(?)_x)((?)_t+bt^k(?)_x)u-ct^{k-1}(?)_xu=0 and proves that the secondmixed problem has a unique solution u(x,t)∈c if c≠-(b-a)(k+1)j (j=0,1,…); whenc=-(b-a)(k+1)j,the existence and uniqueness of solution are lost. Then the author gives the sufficient and necessary conditions for existence of solution, and proves the existence and uniqueness of solution for a modified problem. Finally the solvability for Cauchy problem by means of the methods of extension is discussed.

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更新日期/Last Update: 2013-05-01