| Title:
|
On the mixed problem for hyperbolic partial differential-functional equations of the first order (English) |
| Author:
|
Człapiński, Tomasz |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
791-809 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the mixed problem for the hyperbolic partial differential-functional equation of the first order \[ D_xz(x,y) = f(x,y,z_{(x,y)}, D_yz(x,y)), \] where $z_{(x,y)} \: [-\tau ,0] \times [0,h] \rightarrow \mathbb{R}$ is a function defined by $z_{(x,y)}(t,s) = z(x+t, y+s)$, $(t,s) \in [-\tau ,0] \times [0,h]$. Using the method of bicharacteristics and the method of successive approximations for a certain integral-functional system we prove, under suitable assumptions, a theorem of the local existence of generalized solutions of this problem. (English) |
| Keyword:
|
partial differential-functional equations |
| Keyword:
|
mixed problem |
| Keyword:
|
generalized solutions |
| Keyword:
|
local existence |
| Keyword:
|
bicharacteristics |
| Keyword:
|
successive approximations |
| MSC:
|
35A30 |
| MSC:
|
35D05 |
| MSC:
|
35L60 |
| MSC:
|
35R10 |
| idZBL:
|
Zbl 1010.35021 |
| idMR:
|
MR1746704 |
| . |
| Date available:
|
2009-09-24T10:27:37Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127528 |
| . |
| Reference:
|
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| Reference:
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| . |
