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A note on hyperbolic partial differential equations. II. (English) Zbl 0571.35065
[For part I, see ibid. 31, 243-250 (1981; Zbl 0482.35051).]
We use fixed point theorems of Banach and Krasnosel’skij’s type to establish the existence and continuous dependence of the Darboux problem solution for the equation \(\partial^ 2z/\partial x\partial y=f(x,y,z)\) on initial functions and the right-hand side in \({\mathcal L}^*\)-spaces of these parameters.
MSC:
35L10 Second-order hyperbolic equations
35A35 Theoretical approximation in context of PDEs
Citations:
Zbl 0482.35051
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References:
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