【摘要】 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.p-n(1更多还原

【Abstract】 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 u₀ is in L^p₀（Rⁿ） and ‖u₀‖_{B·^{-n（1p0-1p）,∞}p（Rⁿ）} is sufficently small, where p₀=nα2,p>p₀. Under suitable conditions, the uniqueness of the solution is also obtained.更多还原