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Nonnegative solutions of the characteristic initial value problem for linear partial functional-differential equations of hyperbolic type. (English) Zbl 1145.35418

Summary: On the rectangle \(\mathcal D=[a,b]\times[c,d]\), the problem on the existence and uniqueness of a nonnegative solution of the characteristic initial value problem for the equation \[ \frac{\partial^2u(t,x)}{\partial t\, \partial x}=\ell(u)(t,x)+q(t,x) \] is considered, where \(\ell: C(\mathcal D;\mathbb R)\to L(\mathcal D;\mathbb R)\) is a linear bounded operator and \(q\in L(\mathcal D;\mathbb R_+)\).

MSC:

35L20 Initial-boundary value problems for second-order hyperbolic equations
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