Czechoslovak Mathematical Journal, Vol. 49, No. 4, pp. 791-809, 1999

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

Tomasz Czlapinski

Institute of Mathematics, University of Gdansk, Wit Stwosz Str. 57, 80-952 Gdansk, Poland

Abstract: 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 $z_{(x,y)} [-\tau,0] \times[0,h] \rightarrow\Bbb R$ 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.

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

Classification (MSC 1991): 35D05, 35L60, 35R10


Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).

Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.
Subscribers of Springer (formerly Kluwer) need to access the articles on their site, which is http://www.springeronline.com/10587.


[Previous Article] [Next Article] [Contents of This Number] [Contents of Czechoslovak Mathematical Journal]