常微分方程中的反问题

研究某函数或函数组是什么常微分方程的通解或特解,这可以称为常微分方程中的反问题.这类问题,可以用"微分法"来解决.研究这类问题的意义在于通过利用"微分法"及"逆向思维方法"解决反问题的过程来加强对常微分方程理论内涵的深刻理解.     

Integral Equation Method in Electromagnetic-Sounding Inverse Problems

The use of the integral equation method in electromagnetic-sounding inverse problems is considered. Several approaches to the solution of these inverse problems are proposed.     

Inverse Problem for Finding the Order of the Fractional Derivative in the Wave Equation

Mathematical Notes - The paper investigates an inverse problem for finding the order of the fractional derivative in the sense of Gerasimov–Caputo in the wave equation with an arbitrary...     

Localization for a Fast Diffusion Equation with Absorption

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒｗｅｃｏｎｓｉｄｅｒｔｈｅｆａｓｔｄｉｆｕｓｉｏｎｅｑｕａｔｉｏｎｗｉｔｈａｂｓｏｒｐｔｉｏｎｕｔ＝Δｕｍ－ｕｐ（１）ｉｎＱ＝Ｒｎ×（０,＋∞）ｗｉｔｈｔｈｅｉｎｉｔｉａｌｃｏｎｄｉｔｉｏｎｕ（ｘ,...     

Nonlocal Inverse Problem of Finding Unknown Multipliers in the Right-Hand Part of Lavrentiev-Bitsadze Equation

Russian Mathematics - We consider an equation of mixed elliptic-hyperbolic type. The right-hand part of the equation is represented as a product of two functions, each which only depends on one of...     

Infinite-Time Quenching in a Fast Diffusion Equation with Strong Absorption

This work is concerned with the fast diffusion equation , where 0 < m < 1 and κ < 1. A global positive solution is said to quench regularly in infinite time if for some bounded sequence and some , and if for all compact . It is shown that such regular quenching in infinite time occurs for a large class of initial data if κ > m , whereas it is impossible in one space dimension when κ < −m and the solution is radially symmetric and nondecreasing for x > 0.      

Nonlinear Integral Equation of Inverse Scattering Problems of Wave Equation and Iteration

In this paper, we reduce the 1-D, 2-D and 3-D inverse scattering problems of the wave equation into the nonlinear integral equation. The iteration for solving the above integral equations has been considered.     

Parabolic Equations with Large Parameter. Inverse Problems

Mathematical Notes - For an abstract parabolic equation with initial condition and multidimensional parabolic initial-boundary value problem with absolute terms rapidly oscillating in time, inverse...     

非局部反应扩散方程奇摄动问题

本文研究了一类具有非局部初始条件的奇摄动反应扩散问题．在适当的条件下，利用比较定理讨论了问题解的渐近性态．     

Inverse Problem of Finding the Coefficient of the Lowest Term in Two-Dimensional Heat Equation with Ionkin-Type Boundary Condition

Computational Mathematics and Mathematical Physics - We consider an inverse problem of determining the time-dependent lowest order coefficient of two-dimensional (2D) heat equation with Ionkin...     

The Cauchy Problem for a Nonlinear Diffusion Equation with Absorption and Convection

In this paper we construct the large-time solution of the equation which models the effectof nonlinear absorption on thin film flow of a viscous fluidon a sloping bed. For initial data with finite support we showhow the asymptotic structure of the Cauchy problem depends onthe absorption index . An important addition motivation forthe study is to provide a basis for extending the results tothe more general equation which has applications in plasma physics.     

Solvability of the Direct and Inverse Problems for the Nonlinear Schrödinger Equation

In this paper we study rigorous spectral theory and solvability for both the direct and inverse problems of the Dirac operator associated with the nonlinear Schrödinger equation. We review known results and techniques, as well as incorporating new ones, in a comprehensive, unified framework. We identify functional spaces in which both direct and inverse problems are well posed, have a unique solution and the corresponding direct and inverse maps are one to one.Mathematics Subject Classifications (2000) 34A55, 35Q55.     

一类具有非局部反应扩散方程的奇摄动问题

本文讨论一类具非局部反应扩散方程的奇摄动初始边值问题，利用迭代法及微分不等式，研究了初始边值问题的存在唯一及其渐近性态。     

A Characteristic Iteration for Solving Coefficient Inverse Problems of a Wave Equation

In this paper, a characteristic iteration for solving coefficient inverse problems has been presented. This method is stable and fast converging, and may be extended to the 2-D case. Excellent numerical results have been obtained by this method.