Geodesic
Conjugate problem for third order equation with multiple characteristics and positive function on the highest derivative
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 15 (2015) no. 2, pp. 51-59

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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.
Keywords: equations with multiple characteristics, discontinuous coefficients, conjugate problem, regular solutions, existence and uniqueness. 
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     author = {A. I. Kozhanov and S. V. Potapova},
     title = {Conjugate problem for third order equation with multiple characteristics and positive function on the highest derivative},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {51--59},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2015_15_2_a3/}
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A. I. Kozhanov; S. V. Potapova. Conjugate problem for third order equation with multiple characteristics and positive function on the highest derivative. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 15 (2015) no. 2, pp. 51-59. http://geodesic.mathdoc.fr/item/VNGU_2015_15_2_a3/