Transmission problem for odd-order differential equations with two time variables and a varying direction of evolution


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Resumo

The solvability of a boundary value problem for the differential equation \(h\left( x \right){u_t} + {\left( { - 1} \right)^m}\frac{{{\partial ^{2m + 1}}u}}{{\partial {a^{2m + 1}}}} - {u_{xx}} = f\left( {x,t,a} \right)\) is studied in the case where h(x) has a jump discontinuity and reverses its sign on passing through the discontinuity point. Existence and uniqueness theorems are proved in the case of solutions having all Sobolev generalized derivatives involved in the equation.

Sobre autores

A. Kozhanov

Sobolev Institute of Mathematics, Siberian Branch

Autor responsável pela correspondência
Email: kozhanov@math.nsc.ru
Rússia, Novosibirsk, 630090

S. Potapova

Research Institute of Mathematics

Email: kozhanov@math.nsc.ru
Rússia, Yakutsk, 677000

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