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High-order mixed-type differential equations with weighted integral boundary conditions. (English) Zbl 0967.35101

The authors consider mixed problems that include integral conditions for the equation \[ {\partial^2u\over\partial t^2}+ (-1)^\alpha a(t) {\partial^{\alpha+1} u\over\partial x^\alpha\partial t}= f(x,t), \] where \(0< a_0\leq a(t)\leq a_1\). The existence and uniqueness of strong solutions are proved.

MSC:

35M10 PDEs of mixed type
35G10 Initial value problems for linear higher-order PDEs
35B45 A priori estimates in context of PDEs
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