一类三阶伪抛物型方程初边值问题解的存在定理

借助路径提升问题,利用Banach空间吸引盆理论,研究了一类三阶伪抛物型方程初边值问题解的存在唯一性问题,给出其解存在唯一的充分条件,同时证明了一些已有的结论是本文主要定理的推论.     

On Solvability of an Initial-Boundary Value Problem for a Viscoelasticity Model with Fractional Derivatives

We establish the existence and uniqueness (the latter only in the plane case) of a weak solution to an initial-boundary value problem for the system of the equations of motion of a viscoelastic fluid, namely, for the anti-Zener model whose constitutive law contains fractional derivatives. We use the approximation of this problem by a sequence of regularized Navier–Stokes systems and passage to the limit.     

非线性拟抛物型积分微分方程的初边值问题和初值问题

本文研究非线性拟抛物积分微分方程的初边值问题和初值问题。运用Galerkin方程结合能量估计证明了问题的整体强解的生存性、唯一性和稳定性，最后在一定条件下讨论了初边值问题整体解的不存在性和爆破问题。     

一类带非线性边界条件的拟线性抛物方程的第二初边值问题

利用先验估计的方法讨论具非线性第二边界条件的快扩散方程解的存在性、唯一性、稳定性和渐近性.主要结果是:1)存在唯的整体广义解,解连续依赖于初值;2)存在T₀,t<T₀时解是无穷次可微的正则解;3)当t充分大时,解一致收敛到零.     

Initial-Boundary Value Problem for the Reynolds Lubrication Equation

The nonstationary Reynolds equation of the theory of gas lubrication is considered. The existence and uniqueness of a solution to the initial-boundary value problem for this equation are established in the case of sufficiently smooth data. Estimates for the solution are obtained for large bearing numbers. Bibliography: 8 titles.     

非线性扰动偏微分方程混合边值问题的可解性

研究具有混合边界条件的非线性扰动偏微分摄动方程的可解性.得到原问题的摄动解并证明解的展开式的一致有效性.     

The Phase Space of an Initial-Boundary Value Problem for the Hoff Equation

The Hoff equation describes the H-beam buckling dynamics. We show that the phase space of the Hoff equation is a simple Banach manifold modeled on a subspace complementary to the kernel .     

Global Unique Solvability of an Initial-Boundary Value Problem for the One-Dimensional Barotropic Equations of Binary Mixtures of Viscous Compressible Fluids

Journal of Applied and Industrial Mathematics - We consider the equations of a multivelocity model of a binary mixture of viscous compressible fluids (the two-fluid medium) in the case of...     

Solvability of a Boundary Value Problem for a Differential Equation of the Boussinesq Type

We study the solvability and the construction of the solution of a boundary value problem with a nonlocal integral boundary condition for a three-dimensional analog of the fourth-order homogeneous Boussinesq type differential equation. Separation of variables is used to derive a criterion for the unique solvability of this nonlocal problem. The problem is also considered in the case of violation of the unique solvability criterion.     

Blow up for Initial-Boundary Value Problem of Wave Equation with a Nonlinear Memory in 1-D

The present paper is devoted to studying the initial-boundary value problem of a 1-D wave equation with a nonlinear memory: u_(tt) - u_(xx) = 1/ Γ(1 - γ) ∫_0~t (t - s)~(-γ)|u(s)|~pds. The blow up result will be established when p 1 and 0 γ 1, no matter how small the initial data are, by introducing two test functions and a new functional.     

Theoretical and Numerical Analysis of an Initial-Boundary Value Problem for the Radiative Transfer Equation with Fresnel Matching Conditions

A Cauchy problem for the time-dependent radiative transfer equation in a three-dimensional multicomponent medium with generalized matching conditions describing Fresnel reflection and refraction at the interface of the media is considered. The unique solvability of the problem is proven, a Monte Carlo method for solving the initial-boundary value problem is developed, and computational experiments for different implementations of the algorithm are conducted.     

一类多维非线性拟抛物方程的初边值问题

本文将二阶线性椭圆方程的已知结果与压缩映像原理结合研究任意维数的非线性拟抛物方程的初边值问题，讨论了解的光滑性渐近性质与ｂｌｏｗ－ｕｐ，推广了很多已知结果。     

一具有阻尼非线性双曲型方程初边值问题整体解的不存在性

本文证明一具有阻尼非线性双曲型方程初边值问题局部广义解的存在性和唯一性,并给出此问题解爆破的充分条件.     

Solvability of Nonlocal Boundary Value Problems for an Equation of Mixed Type with Various Boundary Conditions

Two boundary value problems in which one of the conditions is nonlocal and contains a real parameter are studied for an equation of mixed type in a half-strip. Sufficient conditions for the unique solvability of these problems are obtained under some restrictions on the parameter.     

Solvability of a Mixed Nonlocal Problem for a Nonlinear Singular Viscoelastic Equation

The present paper deals with a nonlinear viscoelastic equation having a dissipation term. With the equation some classical and non classical boundary conditions are combined. Based on some a priori bounds, iteration processes and density arguments, we simultaneously solve the nonlinear and the associated linear problems.     

一类三阶非线性伪抛物方程的初边值问题

非线性伪抛物方程由于其来源于一些重要的物理过程而成为研究热点.对于一类三阶非线性伪抛物方程的初边值问题,给出了Hilbert空间中相应的强制不等式,利用同胚理论及推广的反函数定理,得到了非线性方程初边值问题解的大范围存在定理.对于相应的半线性方程给出了初边值问题解的大范围存在性、唯一性定理.     

Conditions for Correct Solvability of a Simplest Singular Boundary Value Problem

We consider a boundary value problem where f(x) ∈ L_p(R), p ∈ [1,∞] (L_∞(R) ≔ C(R) and 0 ≤ q(x) ∈ L^loc₁( R). Boundary value problem (0.1) is called correctly solvable in the given space L_p(R) if for any f(x) ∈ L_p(R) there is a unique solution y(x) ∞ L_p(R) and the following inequality holds with absolute constant c(p) ∈ (0,∞). We find criteria for correct solvability of the problem (0.1) in L_p(R).