On an infinite sequence of invariant measures for the cubic nonlinear Schrödinger equation.
On an initial inverse problem in nonlinear heat equation associated with time-dependent coefficient
In this paper, a nonlinear backward heat problem with time-dependent coefficient in the unbounded domain is investigated. A modified regularization method is established to solve it. New error estimates for the regularized solution are given under some assumptions on the exact solution.
On an initial-boundary value problem for the equation
On an initial-boundary value problem for the nonlinear Schrödinger equation.
On an initial-boundary value problem for the parabolic system which appears in free boundary problems for compressible Navier-Stokes equations [Book]
On an initial-value problem for a nonlinear transport equation in polymer chemistry
On an integral equation in the problem of the diffraction of a plane wave by a transparent circular cone.
On an integral inequality in n-independent variables.
On an integral inequality with a kernel singular in time and space.
On an internal approximation of a class of elliptic eigenvalue problems
On an inverse problem for a linear hyperbolic integrodifferential equation.
On an oblique derivative problem involving an indefinite weight
In this paper we derive results concerning the angular distrubition of the eigenvalues and the completeness of the principal vectors in certain function spaces for an oblique derivative problem involving an indefinite weight function for a second order elliptic operator defined in a bounded region.
On an ODE Relevant for the General Theory of the Hyperbolic Cauchy Problem
2000 Mathematics Subject Classification: 34E20, 35L80, 35L15.In this paper we study an ODE in the complex plane. This is a key step in the search of new necessary conditions for the well posedness of the Cauchy Problem for hyperbolic operators with double characteristics.
On an optimal control problem
On an optimal control problem for a quasilinear parabolic equation
An optimal control problem governed by a quasilinear parabolic equation with additional constraints is investigated. The optimal control problem is converted to an optimization problem which is solved using a penalty function technique. The existence and uniqueness theorems are investigated. The derivation of formulae for the gradient of the modified function is explainedby solving the adjoint problem.
On an optimal decomposition in Zygmund spaces.
On an over-determined problem of free boundary of a degenerate parabolic equation
This work is concerned with the inverse problem of determining initial value of the Cauchy problem for a nonlinear diffusion process with an additional condition on free boundary. Considering the flow of water through a homogeneous isotropic rigid porous medium, we have such desire: for every given positive constants and , to decide the initial value such that the solution satisfies , where . In this paper, we first establish a priori estimate and a more precise Poincaré type inequality...
On analysis of quasihyperbolic equations of linear viscoelasticity
On analytic solutions to the generalized Cauchy problem with data on three surfaces for a quasilinear system.
On analyticity in homogeneous first order partial differential equations