Botyuk A. O.
Ukr. Mat. Zh. - 1997. - 49, № 12. - pp. 1690–1693
We study a periodie boundary-value problem for the quasilinear equation u tt − u xx = F[u, u t , u x ]. We find conditions under which a theorem on the uniqueness of a solution is true.
Ukr. Mat. Zh. - 1997. - 49, № 7. - pp. 998–1001
We study the boundary-value perlodic problem u tt −u xx =F(x, t), u(0, t)=u(π, t)=0, u(x, t+T)=u(x, t), (x, t) is R 2. By using the Vejvoda-Shtedry operator, we determine a solution of this problem.
Ukr. Mat. Zh. - 1997. - 49, № 2. - pp. 302–308
We investigate the linear periodic problem u tt −u xx =F(x, t), u(x+2π, t)=u(x, t+T)=u(x, t), ∈ ℝ2, and establish conditions for the existence of its classical solution in spaces that are subspaces of the Vejvoda-Shtedry spaces.