关于一类分数阶扩散型方程解的适定性

摘要

应用Young不等式、插值不等式和压缩映像原理,研究了一类分数阶耗散型方程解的存在唯一性,得到当初值足够小时,相应的非线性初值问题存在唯一解属于L∞（RN）或L1（RN）∩L∞（RN）.%In this paper,by applying Young inequality,interpolation inequality and contraction mapping principle,we studied a class of fractional dissipation type equations.When the initial value is small enough,the initial value problem to the nonlinear equation has a unique solution in the spaces L∞（RN）or L1（RN）∩L∞（RN）.