Robin Boundary Value Problem for One-Dimensional Landau–Lifshitz Equations

In this paper, we are concerned with the existence and uniqueness of global smooth solution for the Robin boundary value problem of Landau-Lifshitz equations in one dimension when the boundary value depends on time t. Furthermore, by viscosity vanishing approach, we get the existence and uniqueness of the problem without Gilbert damping term when the boundary value is independent of t.     

SINGULAR PERTURBATION OF ROBIN BOUNDARY VALUE PROBLEM FOR THIRD ORDER NONLINEAR SYSTEM WITH BOUNDARY PERTURBATION

ＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＯＦＲＯＢＩＮＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＦＯＲＴＨＩＲＤＯＲＤＥＲＮＯＮＬＩＮＥＡＲＳＹＳＴＥＭＷＩＴＨＢＯＵＮＤＡＲＹＰＥＲＴＵＲＢＡＴＩＯＮ（黄晓秋）福建师范大学福清分校，邮编：３５０３００Ｈ...     

A Robin–Dirichlet problem for a nonlinear wave equation with the source term containing a nonlinear integral

In this paper, we consider the Robin–Dirichlet problem for a nonlinear wave equation with the source term containing a nonlinear integral. Using the Faedo–Galerkin method and the linearization method for nonlinear terms, we prove the existence and uniqueness of a weak solution. We also discuss an asymptotic expansion of high order in a small parameter of a weak solution.     

一类拟线性双曲型方程组混合初-边值问题的半整体C~1解

本文证明了具零特征且形式更广泛的一类拟线性双曲型方程组的具有一般非线性边界条件的混合初 一边值问题半整体C1解的存在唯一性.     

奇异非线性二阶三点边值问题正解的存在唯一性

本文研究了一类奇异非线性二阶三点边值问题，通过摄动技巧和比较原理获得了所论问题正解的存在唯一性。     

一类具有边界摄动的非线性非局部反应扩散方程奇摄动问题

研究了一类具有边界摄动的非线性非局部反应扩散方程奇摄动Robin初始边值问题．在适当的条件下,首先求出了原问题的外部解,然后利用伸长变量、合成展开法和幂级数展开理论构造出解的初始层项,并由此得到解的形式渐近展开式．最后利用微分不等式理论,讨论了问题解的渐近性态并导出了几个有关的不等式,讨论了原问题解的存在唯一性和解的一致有效的渐近估计式．     

源于DNA的非线性波动方程组的Cauchy问题(英文)

本文首先证明源于DNA的非线性波动方程组的周期边值问题局部古典解的存在性和唯一性.其次通过周期边值问题序列证明这个方程组的Cauchy问题存在唯一的局部古典解.     

具有边界摄动的非线性非局部反应扩散方程的奇摄动问题

A class of nonlinear nonlocal singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained; secondly, by using the stretched variable, the composing expansion method and the expanding theory of power series, the initial layer is constructed; and finally, by using the theory of differential inequalities the asymptotic behavior of solutions for initial boundary value problems is studied, and including some relational inequalities the existence and uniqueness of solutions for the original problem and the uniformly valid asymptotic estimation are discussed.     

Existence and iterative method for some fourth order nonlinear boundary value problems

This work is devoted to proving the existence of the iterative solution to a fourth order boundary value problem. By the use of a novel efficient method for nonlinear fourth order boundary value problem, the existence and uniqueness of solution for the problem is obtained. The monotony of iterations is also considered. Some examples are presented to illustrate the main results.     

非线性非局部反应扩散方程奇摄动问题

研究了一类具有非线性非局部反应扩散方程奇摄动Robin初始边值问题。在适当的条件下,首先求出了原问题的外部解,然后利用伸长变量、合成展开法和幂级数展开理论构造出解的初始层项,并由此得到解的形式渐近展开式。最后利用微分不等式理论,讨论了问题解的渐近性态并导出了几个有关的不等式,讨论了原问题解的存在唯一性和解的一致有效的渐近估计式。     

GLOBAL EXISTENCE OF WEAKLY DISCONTINUOUS SOLUTIONS TO A KIND OF MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS

In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {（t, x） ｜ t ≥ 0, x ≥0} is considered. A sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.     

Persistency of wellposedness of Ventcel’s boundary value problem under shape deformations

Ventcel boundary conditions are second order differential conditions that appear in asymptotic models. Like Robin boundary conditions, they lead to well-posed variational problems under a sign condition of the coefficient. This is achieved when physical situations are considered. Nevertheless, situations where this condition is violated appeared in several recent works where absorbing boundary conditions or equivalent boundary conditions on rough surfaces are sought for numerical purposes. The well-posedness of such problems was recently investigated: up to a countable set of parameters, existence and uniqueness of the solution for the Ventcel boundary value problem holds without the sign condition. However, the values to be avoided depend on the domain where the boundary value problem is set. In this work, we address the question of the persistency of the solvability of the boundary value problem under domain deformation.     

The tubular catalyst reactor and the robin problem

In this paper, the model of chemical reaction experiments on a tubular catalyst reactor is discussed. We obtain the existence of the solution and discuss its uniqueness. Furthermore, in view of mathematical interest, we also consider the Robin problem for this nonlinear system.     

在分段区域上的两参数奇摄动非线性方程的ROBIN问题

讨论一类在分段区域上的两参数奇异摄动非线性Robin边值问题。利用算子理论和不动点原理，得到了相应问题解的存在性和唯一性。     

On periodic solutions of nonlinear second order differential systems

The paper deals with the second order differential systems with periodic boundary conditions. In the first part of the paper four different methods are employed to find the unique solution of the linear systems. One of the methods is a shooting type which converts the periodic boundary value problem into its equivalent initial value problem. In the second part of the paper several sufficient conditions are provided for the existence and uniqueness for the nonlinear systems. The technique developed for the linear systems to convert into its equivalent initial value problem is used in an iterative way for the nonlinear systems. It is shown that the iterations converge quadratically.     

一类非线性四阶椭圆型方程边值问题解的存在唯一性

借助路径提升问题,利用Banach空间吸引盆理论研究了四阶椭圆型方程边值问题解的存在唯一性,并给出了其解存在唯一的充分条件.文中主要结果为椭圆型方程解的理论研究提供了一类方法,也推广了Alexiades和Elcrat的有关工作.     

Initial Boundary Value Problem for A Generalized Nonlinear Telegraph Equation with Nonlinear Damping北大核心CSCD

In this paper, the existence and uniqueness of the global generalized solution and the global classical solution of the initial boundary value problem for the generalized nonlinear telegraph equation with nonlinear damping © 2022 Chinese Academy of Sciences. All rights reserved.     

The radiative transfer equation with a nonhomogeneous reflectivity boundary condition coupled with the heat conduction equation

In this paper, we make a rigorous mathematical analysis of the radiative heating of a semitransparent body made of a glass by a black radiative source surrounding it. This requires the study of the coupling between quasi‐steady radiative‐transfer boundary value problems with nonhomogeneous reflectivity boundary conditions (one for each wavelength band in the semitransparent electromagnetic spectrum of the glass) and a nonlinear heat‐conduction evolution equation with a nonlinear Robin boundary condition, which takes into account those wavelengths for which the glass behaves like an opaque body. We prove existence and uniqueness of the solution and give also uniform bounds on the solution, ie, on the absolute temperature distribution inside the body and on the radiative intensities.     

Concave solutions of a general self-similar boundary layer problem for power-law fluids

In this paper, we give a rigorous mathematical analysis for a third order nonlinear boundary value problem. The boundary value problem can be applied to steady free convection around a vertical impermeable flat plate in a fluid-saturated porous medium, or steady flow of a power-law fluid induced by impermeable stretching walls in the frame of boundary layer approximation. We establish the uniqueness, existence and nonexistence of (normal) concave solutions or generalized concave solutions to the problem, and obtain some results about boundedness and asymptotic behavior of the (normal) concave solution or the generalized concave solution.