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Infinite systems of hyperbolic differential-functional inequalities. (English) Zbl 1103.35100
Summary: The paper deals with systems of hyperbolic differential-functional inequalities related to initial value problem on the generalized Haar pyramid for equations \[ \partial_tz_\lambda(t,x)=f_\lambda\bigl(t,x,z, \partial_xz_\lambda(t,x)\bigr),\;\lambda\in\Lambda, \] where \((t,x)= (t,x_1,\dots,x_n)\), \(z=\{z_\lambda\}_{\lambda \in\Lambda}\) and \(\Lambda\) is a compact set of indices. A theorem on strong differential-functional inequalities is the main result of the paper. Extremal solutions of initial value problems for infinite systems of ordinary differential-functional equations are used in the proof of a theorem on weak partial differential-functional inequalities.
MSC:
35R45 Partial differential inequalities and systems of partial differential inequalities
35R10 Functional partial differential equations
34K06 Linear functional-differential equations
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