Page 641 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 641
MATHEMATICAL PHYSICS
References
[1] Lodizhenskaya O.A., The Mathematical Theory of Viscous Incompressible Fluid , Gor-
don and Breach, New York, USA, 1969.
[2] Charls L. Fefferman, Existence and Smoothness of the Navier — Stokes Equation,
Preprint, Princeton Univ., Math. Dept., Princeton, New Jzersy, USA, 2000, pp. 1-5.
[3] Koptev A.V., Integrals of Motion of an Incompressible medium Flow. From Classic to
Modern. In book: Handbook on Navier — Stokes Equations. Theory and Applied Analysis
, Nova Science Rublishers, New York, USA 2017, pp.443-460.
[4] Koptev A.V., Systematization and analysis of integrals of motion for an incompressible
fluid flow, Jour. of Siberian Federal Univ., Math. and Phys., 2018, 11(3), P. 370-382.
[5] Koptev A.V., Exact solutions of 3D Navier — Stokes equations, Jour. of Siberian Federal
Univ., Math. and Phys., 2020, 13(3), P. 306-313.
[6] Koptev A.V., Method for Solving the Navier — Stokes and Euler Equations of Motion for
Incompressible Media, Jour. of Mathematical Sciences, Springer, New York, USA., 2020,
Vol. 250(1), P. 254-382.
Removable singularities for anisotropic porous medium equations
Savchenko (Shan) Mariia, shan_maria@ukr.net
Institute of Applied Mathematics and Mechanics of NAS of Ukraine,
Vasyl’ Stus Donetsk National University, Ukraine
This paper is devoted to the obtaining conditions for removable singularity at the point for
solutions of quasilinear parabolic equations model of which are
n
ut − umi−1uxi = 0, (1)
xi
i=1
n
ut − umi−1uxi xi + f (u) = 0, (2)
(3)
i=1
∂u − n n
∂t
umi−1uxi + |uxi |qi = 0,
xi
i=1 i=1
We focus on the solutions which satisfy the initial condition
u(x, 0) = 0, x ∈ Ω \ {0}, (4)
where Ω is a bounded domain in Rn, n ≥ 2, t ∈ (0, T ), 0 < T < +∞, 0 ∈ Ω.
We suppose that the exponents mi, qi i = 1, n satisfy the following condition
2 2 1n
1 − < m1 ≤ m2 ≤ ... ≤ mn < m + ,m = mi,
n n n
i=1
639
References
[1] Lodizhenskaya O.A., The Mathematical Theory of Viscous Incompressible Fluid , Gor-
don and Breach, New York, USA, 1969.
[2] Charls L. Fefferman, Existence and Smoothness of the Navier — Stokes Equation,
Preprint, Princeton Univ., Math. Dept., Princeton, New Jzersy, USA, 2000, pp. 1-5.
[3] Koptev A.V., Integrals of Motion of an Incompressible medium Flow. From Classic to
Modern. In book: Handbook on Navier — Stokes Equations. Theory and Applied Analysis
, Nova Science Rublishers, New York, USA 2017, pp.443-460.
[4] Koptev A.V., Systematization and analysis of integrals of motion for an incompressible
fluid flow, Jour. of Siberian Federal Univ., Math. and Phys., 2018, 11(3), P. 370-382.
[5] Koptev A.V., Exact solutions of 3D Navier — Stokes equations, Jour. of Siberian Federal
Univ., Math. and Phys., 2020, 13(3), P. 306-313.
[6] Koptev A.V., Method for Solving the Navier — Stokes and Euler Equations of Motion for
Incompressible Media, Jour. of Mathematical Sciences, Springer, New York, USA., 2020,
Vol. 250(1), P. 254-382.
Removable singularities for anisotropic porous medium equations
Savchenko (Shan) Mariia, shan_maria@ukr.net
Institute of Applied Mathematics and Mechanics of NAS of Ukraine,
Vasyl’ Stus Donetsk National University, Ukraine
This paper is devoted to the obtaining conditions for removable singularity at the point for
solutions of quasilinear parabolic equations model of which are
n
ut − umi−1uxi = 0, (1)
xi
i=1
n
ut − umi−1uxi xi + f (u) = 0, (2)
(3)
i=1
∂u − n n
∂t
umi−1uxi + |uxi |qi = 0,
xi
i=1 i=1
We focus on the solutions which satisfy the initial condition
u(x, 0) = 0, x ∈ Ω \ {0}, (4)
where Ω is a bounded domain in Rn, n ≥ 2, t ∈ (0, T ), 0 < T < +∞, 0 ∈ Ω.
We suppose that the exponents mi, qi i = 1, n satisfy the following condition
2 2 1n
1 − < m1 ≤ m2 ≤ ... ≤ mn < m + ,m = mi,
n n n
i=1
639
