Classical Solvability of the First Initial Boundary-Value Problem for a Nonlinear Strongly Degenerate Parabolic Equation

We prove the existence of a classical solution global in time for the first initial boundary-value problem for a nonlinear strongly degenerate parabolic equation.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 10, pp. 1299 – 1320, October, 2004.     

On the Restoration of Initial Data of a Boundary-Value Problem for a Second-Order Parabolic Equation

On the basis of the Fourier expansion of a generalized function in a complete orthonormal system of fundamental functions of an elliptic operator, we propose an approximate method for determination of the initial data of a boundary-value problem for a second-order parabolic equation.     

Uniqueness of Solution to the First Initial Boundary Value Problem for Parabolic Systems on the Plane in a Model Case

The first initial boundary value problem for a one-dimensional (in x) Petrovskii parabolic second-order system with constant coefficients in a semibounded (in x) domain with a nonsmooth lateral boundary is proved to have a unique classical solution in certain Hölder classes.     

Generalized Solution of the First Boundary Value Problem for Parabolic Monge-Ampere Equation

The existence and uniqueness of generalized solution to the first boundary value problem for parabolic Monge-Ampère equation - ut det D²_xu = f in Q = Ω × (0, T], u = φ on ∂_pQ are proved if there exists a strict generalized supersolution u_φ, where Ω ⊂ R^n is a bounded convex set, f is a nonnegative bounded measurable function defined on Q, φ ∈ C(∂_pQ), φ(x, 0) is a convex function in \overline{\Omega}, ∀x_0 ∈ ∂Ω, φ(x_0, t) ∈ C^α([0, T]).     

An Approach to the Solution of the Initial Boundary-Value Problem for Systems of Fourth-Order Hyperbolic Equations

Mathematical Notes - The forms of the Segre cubic over non-algebraically closed fields, their automorphisms groups, and equivariant birational rigidity are studied. In particular, it is shown that...     

On the Asymptotic Behavior of Solutions of the First Initial Boundary-Value Problems for Parabolic Equations

We consider the first initial boundary-value problem for a strongly parabolic system on an infinite cylinder with nonsmooth boundary. We prove some results on the existence, uniqueness, and asymptotic behavior of solutions as t .     

The Initial Boundary-Value Problem for a Generalized Stokes System in a Half-Space

The paper contains the construction of a solution of the Cauchy–Dirichlet problem in the half-space for a family of systems of differential equations that includes a Stokes system. For this solution, coercive estimates in the Hölder spaces of functions are obtained. Bibliography: 12 titles.     

Contact Problem for Second Order Parabolic Systems in a Strip with a Nonsmooth Interface Curve

Differential Equations - We prove the existence of a classical solution of the contact problem for Petrovskii parabolic systems of the second order with Dini continuous coefficients in a strip...     

Rapidly Decreasing Solution of the Initial Boundary-Value Problem for the Toda Lattice

Using the inverse scattering transform, we investigate an initial boundary-value problem with zero boundary condition for the Toda lattice. We prove the existence and uniqueness of a rapidly decreasing solution and determine a class of initial data that guarantees the existence of a rapidly decreasing solution. __________ Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 8, pp. 1144 – 1152, August, 2005.     

具时滞的半线性抛物问题

基于C.C.Travis和G.F.Webb等人对时滞问题的研究,作者曾在[5]中对一类被称为带正时滞臂的时滞抛物型问题进行了讨论。本文在[5]的基础上继续讨论此类问题。对于抽象时滞问题,在非线性项满足局部Lip连续(甚至对某些变元仅仅是H?lder连续)及一定的增长性限制的条件下,我们对非线性项作了较精细的估计,用半群方法得到了解的存在性和唯一性。进一步,对带零时滞臂的抛物型问题,我们先用上面的结果建立逼近方程,用紧性方法在较弱的条件下也得到了解的存在性。 其次,我们将所得到的抽象结果应用于二阶时滞抛物型     

L p -Estimates for Solutions to the Initial Boundary-Value Problem for the Generalized Stokes System in a Bounded Domain

The main result of the paper is the proof of the solvability in anisotropic Sobolev spaces. Bibliography: 23 titles.     

Existence and Uniqueness of a Weak Solution to the Initial Mixed Boundary-Value Problem for Quasilinear Elliptic-Parabolic Equations

We prove the existence and the uniqueness of a weak solution to the mixed boundary problem for the elliptic-parabolic equation

Necessary and Sufficient Conditions of Stabilization of Solutions of the First Boundary-Value Problem for a Parabolic Equation

Necessary and sufficient conditions are established for the stabilization of the solution of the first boundary-value problem for a divergent second-order parabolic equation with no lower-order terms. For an arbitrary (possibly unbounded) domain Q ? ? ^N , N?≥?3, with an initial function u ₀(x) defined in Q for t?=?0, one studies the influence of Q on the stabilization of the solution in the cylinder Z?=?Q?×?[0,∞) with the homogeneous boundary conditions on the lateral surface of Z.     

Uniqueness of Solutions to Initial Boundary Value Problems for Parabolic Systems in Plane Bounded Domains with Nonsmooth Lateral Boundaries

Doklady Mathematics - We consider initial boundary value problems with boundary conditions of the first or second kind for one-dimensional (with respect to a spatial variable) Petrovskii parabolic...