The One-Dimensional Heat Equation: Preface
The One-Dimensional Heat Equation: Preface
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DOI：
10.1017/cbo9781139086967.004
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发表时间：
1984
期刊：
影响因子：
--
通讯作者：
J. Cannon;F. Browder
中科院分区：
文献类型：
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作者：
J. Cannon;F. Browder
编者按前言1.导言2.柯西问题3.初值问题4.具有温度边界规范的四分之一平面的初边值问题5.具有热流边界规范的四分之一平面的初边值问题6.具有温度边界规范和热流边界规范的半无限长条的初边值问题7.半无限长条的某些初边值问题的约化积分方程组：一些练习8.积分方程组9.边值问题的解和周期解10.解的解析性11.一些状态估计问题对数据的连续依赖性12.一些状态估计问题的一些数值方法13.由超定数据确定未知的随时间变化的扩散系数a(T)14.具有Holder连续边界的一般区域的初值和/或边值问题15.一般区域解的一些性质16.具有温度-边界规范的一般区域的解：Perron-Poincare方法17.具有温度边界规范的单相Stefan问题18.具有流量边界规范的单相Stefan问题：一些练习19.非齐次热方程ut=uxx+f(x，T)20.非齐次热度方程的应用：方程ut=uxx+f(x，t，u，ux)符号索引主题索引。
Editor's statement Foreword Felix E. Browder Preface Preliminaries 1. Introduction 2. The Cauchy problem 3. The initial-value problem 4. The initial-boundary-value problem for the quarter plane with temperature-boundary specification 5. The initial-boundary-value problem for the quarter plane with heat-flux-boundary specification 6. The initial-boundary-value problem for the semi-infinite strip with temperature-boundary specification and heat-flux-boundary specification 7. The reduction of some initial-boundary-value problems for the semi-infinite strip, to integral equations: some exercises 8. Integral equations 9. Solutions of boundary-value problems for all times and periodic solutions 10. Analyticity of solutions 11. Continuous dependence upon the data for some state-estimation problems 12. Some numerical methods for some state-estimation problems 13. Determination of an unknown time-dependent diffusivity a(t) from overspecified data 14. Initial- and/or boundary-value problems for gneral regions with Holder continuous boundaries 15. Some properties of solutions in general domains 16. The solution in a general region with temperature-boundary specification: the method of perron-poincare 17. The one-phase stefan problem with temperature-boundary specification 18. The one-phase stefan problem with flux-boundary specification: some exercises 19. The inhomogeneous heat equation ut=uxx+f(x,t) 20. An application of the inhomogeneous heat equation: the equation ut=uxx+f(x,t,u,ux) Symbol index Subject index.