一类边值条件下的热方程的形式解

`The formal solution of heat equation with a class of boundary value condition

目的扩展与Sturm-Liouville问题密切相关的热方程的边值条件,并对其求解。方法将某类具体边值条件进行线形组合,扩展为形如-α1ux(0,t)+β1u(0,t)=g1(t),α2ux(l,0)+β2u(l,t)=g2(t)的边值条件,然后利用比较系数法求边值条件下热方程的解。结果求得扩展边值条件下热方程的形式解。结论给出某一大类边值条件下与Sturm-Liouville问题密切相关的热方程普遍意义上的形式解。

Aim To extend boundary value conditions of heat equation that is closely related to Sturm-Liouville problem and find the corresponding solution.Methods Linear combination of specific boundary value conditions are extended to be such boundary value conditions as-α1ux（0,t）＋β1u（0,t）=g1（t）,α2ux（l,0）＋β2u（l,t）=g2（t）,and then the solution of the heat equation under the certain boundary value conditions is sought with the comparison coefficient method.Results The formal solution of heat equation with extended boundary value conditions is found.Conclusion The general formal solution of heat equation with a wide class of extended boundary value condition is given in this paper.