Conjugate problem for third order equation with multiple characteristics and positive function on the highest derivative

A. I. Kozhanov   ; S. V. Potapova

Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 15 (2015) no. 2, pp. 51-59

Résumé

The conjugate problem (generalized diffraction problem) is studied for third order equation $u_{t}-h(x)u_{xxx}+c(x,t)u=f(x,t)$, where coefficient $h(x)$ is positive and may have a discontinuity of the first kind at the point $x=0$. The existence and uniqueness of regular solutions are established.

Détail

Keywords: equations with multiple characteristics, discontinuous coefficients, conjugate problem, regular solutions, existence and uniqueness.

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