On the initial value problem for a partial differential equation with operator coefficients
In the present work it is studied the initial value problem for an equation of the form L∂ku∂tk=∑j=1kLj∂k−ju∂tk−j,where L is an elliptic partial differential operator and (Lj:j=1,…,k) is a family of partial differential operators with bounded operator coefficients in a suitable function space. It is...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1980-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171280000075 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849402880436469760 |
|---|---|
| author | Mahmoud M. El-Borai |
| author_facet | Mahmoud M. El-Borai |
| author_sort | Mahmoud M. El-Borai |
| collection | DOAJ |
| description | In the present work it is studied the initial value problem for an equation of the form L∂ku∂tk=∑j=1kLj∂k−ju∂tk−j,where L is an elliptic partial differential operator and (Lj:j=1,…,k) is a family of partial differential operators with bounded operator coefficients in a suitable function space. It is found a suitable formula for solution. The correct formulation of the Cauchy problem for this equation is also studied. |
| format | Article |
| id | doaj-art-94493b51f12a4add83a956f41b0b3cbf |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1980-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-94493b51f12a4add83a956f41b0b3cbf2025-08-20T03:37:27ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251980-01-013110311110.1155/S0161171280000075On the initial value problem for a partial differential equation with operator coefficientsMahmoud M. El-Borai0Department of Mathematics, King Abdulaziz University, P.O. Box 1540, Jeddah, Saudi ArabiaIn the present work it is studied the initial value problem for an equation of the form L∂ku∂tk=∑j=1kLj∂k−ju∂tk−j,where L is an elliptic partial differential operator and (Lj:j=1,…,k) is a family of partial differential operators with bounded operator coefficients in a suitable function space. It is found a suitable formula for solution. The correct formulation of the Cauchy problem for this equation is also studied.http://dx.doi.org/10.1155/S0161171280000075partial differential equationselliptic operatorsCauchy problems and general solutions. |
| spellingShingle | Mahmoud M. El-Borai On the initial value problem for a partial differential equation with operator coefficients International Journal of Mathematics and Mathematical Sciences partial differential equations elliptic operators Cauchy problems and general solutions. |
| title | On the initial value problem for a partial differential equation with operator coefficients |
| title_full | On the initial value problem for a partial differential equation with operator coefficients |
| title_fullStr | On the initial value problem for a partial differential equation with operator coefficients |
| title_full_unstemmed | On the initial value problem for a partial differential equation with operator coefficients |
| title_short | On the initial value problem for a partial differential equation with operator coefficients |
| title_sort | on the initial value problem for a partial differential equation with operator coefficients |
| topic | partial differential equations elliptic operators Cauchy problems and general solutions. |
| url | http://dx.doi.org/10.1155/S0161171280000075 |
| work_keys_str_mv | AT mahmoudmelborai ontheinitialvalueproblemforapartialdifferentialequationwithoperatorcoefficients |