Abstract
We prove the existence and uniqueness of a solution of a mixed problem for a system of pseudoparabolic equations in an unbounded (with respect to space variables) domain.
Similar content being viewed by others
REFERENCES
H. Gajewski, K. Gröger, and K. Zacharias, Nichtlineare Operatorengleichungen und Operatorendifferentialgleichungen Akademie, Berlin (1974).
R. E. Showalter, “Pseudoparabolic partial differential equations,” Dissert. Abstrs. B29, No. 8, 2994 (1968).
R. E. Showalter, “Partial differential equations of Sobolew — Galperin type,” Pacif. J. Math. 31, No. 3, 787–793 (1969).
S. I. Lyashko, “An analog of the Galerkin method for the solution of pseudoparabolic equations,” Dopov. Akad. Nauk Ukr. SSR No. 8, 54–55 (1991).
I. I. Lyashko, S. I. Lyashko, and T. V. Tomashevskaya, “An approximate method for the solution of pseudoparabolic equations,” Dopov. Nats. Akad. Ukr. No. 9, 56–58 (1994).
M. O. Kolin'ko and S. P. Lavrenyuk, “Uniqueness of a solution of the Fourier problem for a nonlinear pseudoparabolic system,” Visn. L'viv. Univ., Ser. Mekh. Mat. Issue 45, 71–77 (1996).
M. O. Bas and S. P. Lavrenyuk, “On the uniqueness of a solution of the Fourier problem for one system of the Sobolev — Gal'perin type,” Ukr. Mat. Zh. 48, No. 1, 124–128 (1996).
S. P. Lavrenyuk and M. B. Ptashnyk, “Pseudoparabolic variational inequalities without initial conditions,” Ukr. Mat. Zh. 50, No. 7, 919–929 (1998).
W. Rundell, “The uniqueness class for the Cauchy problem for pseudoparabolic equations,” Proc. Amer. Math. Soc. 76, No. 2, 253–257 (1979).
G. I. Khil'kevich, “An analog of the Saint-Venant principle, the Cauchy problem, and the first boundary-value problem for pseudoparabolic equations in an unbounded domain,” Usp. Mat. Nauk 36, No. 4, 229–230 (1981).
G. I. Khil'kevich, “On the behavior of solutions of pseudoparabolic equations in a neighborhood of regular points and at infinity,” in: Differential Equations and Applications [in Russian], Moscow University, Moscow (1984), pp. 170–175.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Domans'ka, G.P., Lavrenyuk, S.P. A Mixed Problem for One Pseudoparabolic System in an Unbounded Domain. Ukrainian Mathematical Journal 53, 141–148 (2001). https://doi.org/10.1023/A:1010453220555
Issue Date:
DOI: https://doi.org/10.1023/A:1010453220555