2017
Том 69
№ 9

All Issues

Mixed problem for a semilinear ultraparabolic equation in an unbounded domain

Lavrenyuk S. P., Oliskevych M. O.

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Abstract

We establish conditions for the existence and uniqueness of a solution of the mixed problem for the ultraparabolic equation $$u_t + \sum^m_{i=1}a_i(x, y, t) u_{y_i} - \sum^n_{i,j=1} \left(a_{ij}(x, y, t) u_{x_i}\right)_{x_j} + \sum^n_{i,j=1} b_{i}(x, y, t) u_{x_i} + b_0(x, y, t, u) =$$ $$= f_0(x, y, t, ) - \sum^n_{i=1}f_{i, x_i} (x, y, t) $$ in an unbounded domain with respect to the variables x.

English version (Springer): Ukrainian Mathematical Journal 59 (2007), no. 12, pp 1870-1884.

Citation Example: Lavrenyuk S. P., Oliskevych M. O. Mixed problem for a semilinear ultraparabolic equation in an unbounded domain // Ukr. Mat. Zh. - 2007. - 59, № 12. - pp. 1661–1673.

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