2019
Том 71
№ 9

All Issues

Tedeev A. F.

Articles: 11
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.

↓ Abstract   |   Full text (.pdf)

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.

Chronicles (Ukrainian)

The International Conference “Nonlinear Partial Differential Equations”

Skrypnik I. V., Tedeev A. F.

Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 7. - pp. 1007–1008

Article (Russian)

Two-sided estimates of a solution of the Neumann problem as $t \rightarrow \infty$ for a second-order Quasilinear Parabolic Equation

Tedeev A. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 7. - pp. 989-998

We establish exact upper and lower bounds as $t \rightarrow \infty$ for the norm ‖u(·, t)‖ L ∞(Ω) of a solution of the Neumann problem for a second-order quasilinear parabolic equation in the region D=Ω×{>0}, where Ω is a region with noncompact boundary.

Article (Russian)

Method for symmetrization and estimation of solutions of the Neumann problem for the equation of a porous medium in domains with noncompact boundary for infinitely increasing time

Bazalii B. V., Tedeev A. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1995. - 47, № 2. - pp. 147–157

We consider the initial boundary-value Neumann problem for the equation of a porous medium in a domain with noncompact boundary. By using a symmetrization method, we obtain exactL p-estimates, 1≤p≤∞, for solutions as t→∞.

Article (Ukrainian)

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

Tedeev A. F.

↓ Abstract   |   Full text (.pdf)

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

Article (Russian)

Multiplicative inequalities in domains with noncompact boundary

Tedeev A. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1992. - 44, № 2. - pp. 260–268

Exact embedding theorems of the multiplicative type are established for functions of Sobolev spaces defined in a domain Ω ⊂R n,n⩾2, whose boundary is not compact. The main condition on the domain is of the isoperimetric type.

Chronicles (Russian)

Conferences on nonlinear problems of mathematical physics and problems with free boundaries

Bazalii B. V., Skrypnik I. V., Tedeev A. F.

Full text (.pdf)

Ukr. Mat. Zh. - 1992. - 44, № 2. - pp. 295-297