| Title:
|
On the existence and uniqueness of solution of the Cauchy problem for a class of linear integro-differential equations (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
16 |
| Issue:
|
2 |
| Year:
|
1971 |
| Pages:
|
136-154 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some problems in the theory of viscoelasticity may be described by means of integro-differential equations. In the paper a class of initial-value problems is considered which includes these physical examples, covering also their analogues - equations of the second order in time coordinate. The theory is restricted to the equations only, possessing in the same term both the highest spatial and the highest derivatives.
The weak solution is defined on the base of variational principles, introduced in a previous article, and its existence, uniqueness and continuous dependence on the given data is proved, using the theory of integral Volterra's equations in Banach spaces. () |
| MSC:
|
45D05 |
| MSC:
|
45J05 |
| MSC:
|
45K05 |
| MSC:
|
74D99 |
| idZBL:
|
Zbl 0217.43503 |
| idMR:
|
MR0296633 |
| DOI:
|
10.21136/AM.1971.103337 |
| . |
| Date available:
|
2009-05-07T08:07:50Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103337 |
| . |
| Reference:
|
[1] H. X. Арутюнян: Некоторые вопросы теории ползучести.Москва 1952. Zbl 1145.11324 |
| Reference:
|
[2] I. Hlaváček M. Predeleanu: Sur l'existence et l'unicité de la solution dans la théorie du fluage linéaire.Aplikace matematiky 9 (1964), 321-327, 10 (1965), 391-398, 11 (1966), 199-210. |
| Reference:
|
[3] I. Hlaváček: Variational formulation of the Cauchy problem for equations with operator coefficients.Aplikace matematiky 16 (1971), 1, 46-63. MR 0283652 |
| Reference:
|
[4] С. Г. Михлип: Проблема минимума квадратичного функционала.Москва 1952. Zbl 1145.11324 |
| Reference:
|
[5] I. Hlaváček J. Nečas: On inequalities of Korn's type.Archive for Rational Mechanics and Analysis, 36 (1970), 4, 305-334. MR 0252844, 10.1007/BF00249518 |
| Reference:
|
[6] I. Hlaváček: On the existence and uniqueness of solution of the Cauchy problem for linear integro-differential equations with operator coefficients.Aplikace matematiky 16 (1971), 1, 64-80. MR 0300158 |
| Reference:
|
[7] N. Dunford J. T. Schwartz: Linear operators, Part I. General Theory.Interscience Publishers, 1958. MR 1009162 |
| . |
