-
Article
On the instantaneous shrinking of the support of a solution to the Cauchy problem for an anisotropic parabolic equation
We study the phenomenon of instantaneous shrinking of the support of solution to the Cauchy problem for the parabolic equation with anisotropic degeneration, double nonlinearity, and strong absorption. In term...
-
Article
On one boundary-value problem for a strongly degenerate second-order elliptic equation in an angular domain
We prove the existence and uniqueness of a classical solution of a singular elliptic boundary-value problem in an angular domain. We construct the corresponding Green function and obtain coercive estimates for...
-
Article
Bilateral estimates for the support of a solution of the Cauchy problem for an anisotropic quasilinear degenerate equation
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 initia...
-
Article
Influence of the inhomogeneity of porous media on the instantaneous compactification of the support of solution of the filtration problem
We study the phenomenon of instantaneous compactification and the initial behavior of the support of solution of the filtration equation for inhomogeneous porous media.
-
Article
Stefan problem with a kinetic and the classical conditions at the free boundary
The Stefan problem is considered with the kinetic condition u+=u−=ɛk(y, τ)-ɛv at the phase interface, where k(y, τ) is the half-sum of the principal curvatures of the free boundary and v is the speed of its shift...
-
Article
Solvability of a problem with an unknown boundary between the domains of a parabolic and an elliptic equations
-
Article
Existence of a smooth solution in a filtration problem