2018
Том 70
№ 2

All Issues

Tedeev A. F.

Articles: 6
Article (Russian)

On the behavior of solutions of the Cauchy problem for a degenerate parabolic equation with source in the case where the initial function slowly vanishes

Martynenko A. V., Shramenko V. N., Tedeev A. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 11. - pp. 1500-1515

We study the Cauchy problem for a degenerate parabolic equation with source and inhomogeneous density of the form $$u_t = \text{div}(\rho(x)u^{m-1}|Du|^{\lambda-1}Du) + u ^p $$ in the case where initial function decreases slowly to zero as $|x| \rightarrow \infty$. We establish conditions for the existence and nonexistence of a global-in-time solution, which substantially depend on the behavior of the initial data as $|x| \rightarrow \infty$. In the case of global solvability, we obtain an exact estimate of a solution for large times.

Article (Russian)

Bilateral estimates for the support of a solution of the Cauchy problem for an anisotropic quasilinear degenerate equation

Degtyarev S. P., Tedeev A. F.

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Ukr. Mat. Zh. - 2006. - 58, № 11. - pp. 1477–1486

We establish exact-order bilateral estimates for the size of the support of a solution of the Cauchy problem for a doubly nonlinear parabolic equation with anisotropic degeneration in the case where the initial data are finite and have finite mass.

Article (Russian)

Initial-boundary-value problems for quasilinear degenerate hyperbolic equations with damping. Neumann problem

Tedeev A. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 2. - pp. 272–282

We study the behavior of the total mass of the solution of Neumann problem for a broad class of degenerate parabolic equations with damping in spaces with noncompact boundary. New critical indices for the investigated problem are determined.

Article (Russian)

Theorems on the existence and nonexistence of solutions of the Cauchy problem for degenerate parabolic equations with nonlocal source

Afanaseva N. V., Tedeev A. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 11. - pp. 1443–1464

We consider the Cauchy problem for a doubly nonlinear degenerate parabolic equation with nonlocal source under the assumption that the initial function is integrable. We establish the existence and nonexistence of time-global solutions of the problem.

Article (Ukrainian)

Qualitative properties of solutions of the Neumann problem for a higher-order quasilinear parabolic equation

Tedeev A. F.

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Ukr. Mat. Zh. - 1993. - 45, № 11. - pp. 1571–1579

The property of localization of perturbations is proved for a solution of an initial boundary-value Neumann problem in a regionD=?x, t>0, where ? is a region in Rnwith a noncompact boundary.

Article (Ukrainian)

Symmetrization and initial boundary-value problems for certain classes of nonlinear second order parabolic equations

Bazalii B. V., Tedeev A. F.

Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 884–892