On the solution of reaction-diffusion equations with double diffusivity.
On the solution of Schrödinger-like wave equations
On the solution of some inverse problems in infiltration
In this paper we discuss inverse problems in infiltration. We propose an efficient method for identification of model parameters, e.g., soil parameters for unsaturated porous media. Our concept is strongly based on the finite speed of propagation of the wetness front during the infiltration into a dry region. We determine the unknown parameters from the corresponding ODE system arising from the original porous media equation. We use the automatic differentiation implemented in the ODE solver LSODA....
On the solution of some inverse problems in porous media flow.
On the solution of some non-local problems
This paper deals with two types of non-local problems for the Poisson equation in the disc. The first of them deals with the situation when the function value on the circle is given as a combination of unknown function values in the disc. The other type deals with the situation when a combination of the value of the function and its derivative by radius on the circle are given as a combination of unknown function values in the disc. The existence and uniqueness of the classical solution of these...
On the solution of the Dirichlet problem for an elliptic equation degenerating on the boundary.
On the solution of the heat equation with nonlinear unbounded memory
The paper deals with the question of global solution to boundary value problem for the system of semilinear heat equation for and complementary nonlinear differential equation for (“thermal memory”). Uniqueness of the solution is shown and the method of successive approximations is used for the proof of existence of a global solution provided the condition holds. The condition is verified for some particular cases (e. g.: bounded nonlinearity, homogeneous Neumann problem (even for unbounded...
On the solution of the Liouville equation over a rectangle.
On the solution of the mixed problem (Preliminary communication)
On the solution of the nonlinear wave equation by the decomposition method.
On the solution of transonic flows with weak shocks
On the solution sets of some nonconvex hyperbolic differential inclusions
On the solutions of Knizhnik-Zamolodchikov system
We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions. We prove that under some conditions the solution of the KZ system is rational too. We give the method of constructing the corresponding rational solution. We deduce the asymptotic formulas for the solution of the KZ system when the parameter ρ is an integer.
On the solutions of nonlinear initial-boundary value problems.
On the solvability in Gevrey of a linear operator in two variables.
On the solvability of a class of singular parabolic equations with nonlocal boundary conditions in nonclassical function spaces.
On the solvability of a Darboux type non-characteristic spatial problem for the wave equation.
On the solvability of a multidimensional version of the Goursat problem for a second order hyperbolic equation with characteristic degeneration.
On the solvability of a nonlocal problem arising in dynamics of moisture transfer.
On the solvability of a spatial problem of Darboux type for the wave equation.