热传导方程中带有非线性边界条件和未知系数的Stefan问题  

Stefan Problem in Heat Conduction Equation with An Unknown Coefficient and a Nonlinear Boundary Condition

作　　者：杨枫林[1] 张大力[1] 高广宏[1] 

机构地区：[1]哈尔滨工业大学数学系

出　　处：《哈尔滨工业大学学报》1998年第5期25-29,共5页Journal of Harbin Institute of Technology

基　　金：哈尔滨工业大学基金

摘　　要：对热传导方程中带有非线性边界条件和未知系数的未知边界问题（或Ｓｔｅｆａｎ问题）进行了研究．通过适当的变换，将问题转化成一等价的积分方程组，然后应用压缩映象原理，给出了在一定条件下解的存在性、唯一性和稳定性结果．This paper discusses the problem of determining unknown boundary for heat conduction equation (or Stefan problem) with an unknown coefficient and a nonlinear boundary condition. The problem can be suitably transformed into an equivalent system of integral equations and then, the principle of fixed point is applied to give the results in existence, stability, and uniqueness of the solution under given conditions.

关 键 词：反问题 热传导方程 非线性边界条件 STEFAN问题 

分 类 号：O551.3[理学—热学与物质分子运动论] O175.26[理学—物理]