关于半线性热方程整体解的注记

Note on the global solution to the semilinear heat equation

利用Besov空间的热核刻画及压缩映射原理,研究半线性热方程ut-Δu=u|u|α的初值问题,得到了当初值u0∈Lp0(Rn)且‖u0‖B·p),∞(Rn)(p0=nαp0-12,p>p0)充分小时,整体解的存在性及在一定条件下解的惟一性.

By using the heat kernel characterization of Besov spaces and the contraction mapping principle, the initial problem to the semilinear heat equation u_t-Δu=u|u|~α is studied. The global existence of the solution is proved when the initial value u_0 is in L^(p_0)(R^n) and ‖u_0‖_(B·^(-n(1p_0-1p),∞)_p(R^n)) is sufficently small, where p_0=nα2,p>p_0. Under suitable conditions, the uniqueness of the solution is also obtained.