This dissertation focuses on the locally classical solution and the globally classical solution of one dimensional combustion free boundary problem . the existence and uniqueness of classical solution locally in time will be obtained by the use of fixed point theorem 本文集中于对一个一维燃烧问题的局部古典解和整体古典解进行研究，应用不动点定理得到局部古典解存在唯一性。
