Cauchy problem for a second-order hyperbolic operator-differential equation with a singular coefficient

被引：0
作者：
A. B. Aliev
G. D. Shukyurova
机构：
[1] Azerbaijan Technical University,Institute for Mathematics and Mechanics
[2] National Academy of Sciences,undefined
来源：
Differential Equations | 2011年 / 47卷
关键词：
Hilbert Space; Cauchy Problem; Optimal Control Problem; Hyperbolic Equation; Lipschitz Condition;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In a Hilbert space, we study the well-posedness of the Cauchy problem for a second-order operator-differential equation with a singular coefficient.
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页码：887 / 891
页数：4
相关论文
共 14 条
  • [1] Kato T.(1970)Linear Evolution Equations of “Hyperbolic” Type J. Fac. Sci. Univ. Tokyo 17 241-258
  • [2] Kato T.(1973)Linear Evolution Equations of “Hyperbolic” Type. II J. Math. Soc. Japan 25 648-666
  • [3] Colombini F.(1978)Existence et unicit’e des solutions des’ equations hyperboliques du second order à coefficients ne d’ependant que du temps C. R. Acad. Sci. 286 A.1045-A1048
  • [4] De Giorgi E.(2006)Modulus of Continuity of the Coefficients and Loss of Derivatives in the Strictly Hyperbolic Cauchy Problem J. Differential Equations 221 143-157
  • [5] Spagnolo S.(2002)Well-Posedness of the Cauchy Problem for a Hyperbolic Equation with Non-Lipschitz Coefficients Ann. Sc. Norm. Super. Pisa 1 327-358
  • [6] Cicognani M.(2004)About the Optimality of Oscillations in Non-Lipschitz Coefficients for Strictly Hyperbolic Equations Ann. Sc. Norm. Super. Pisa 3 589-608
  • [7] Colombini F.(1979)The Fourier Method for Certain Singular Hyperbolic Equations Dokl. Akad. Nauk SSSR 248 792-796
  • [8] Colombini F.(1960)On the Solvability of Mixed Problems for Hyperbolic and Parabolic Equations Uspekhi Mat. Nauk 15 98-154
  • [9] Del Santo D.(undefined)undefined undefined undefined undefined-undefined
  • [10] Kinoshita T.(undefined)undefined undefined undefined undefined-undefined
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