On the mixed problem for hyperbolic partial differential-functional equations of the first order

Title:

On the mixed problem for hyperbolic partial differential-functional equations of the first order

Creator:

Człapiński, Tomasz

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:d1f6300b-a57b-4542-92c8-3482113ec459
uuid:d1f6300b-a57b-4542-92c8-3482113ec459

Subject:

partial differential-functional equations, mixed problem, generalized solutions, local existence, bicharacteristics, and successive approximations

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

791-809

Source:

Czechoslovak Mathematical Journal | 1999 Volume:49 | Number:4

Harvested from:

CDK

Metadata only:

false