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On the mixed problem for hyperbolic partial differential-functional equations of the first order
Czechoslovak Mathematical Journal, Tome 49 (1999) no. 4, pp. 791-809 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 35A30, 35D05, 35L60, 35R10
Keywords: partial differential-functional equations; mixed problem; generalized solutions; local existence; bicharacteristics; successive approximations 
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     title = {On the mixed problem for hyperbolic partial differential-functional equations of the first order},
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Człapiński, Tomasz. On the mixed problem for hyperbolic partial differential-functional equations of the first order. Czechoslovak Mathematical Journal, Tome 49 (1999) no. 4, pp. 791-809. http://geodesic.mathdoc.fr/item/CMJ_1999_49_4_a9/

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