摘要
This paper is devoted to a study of L^q-tracing of the fractional temperature field u(t, x)—the weak solution of the fractional heat equation(?_t +(-?_x)~α)u(t, x) = g(t, x) in L^p(R_+^(1+n)) subject to the initial temperature u(0, x) = f(x) in L^p(R^n).
This paper is devoted to a study of L^q-tracing of the fractional temperature field u（t, x）—the weak solution of the fractional heat equation（？_t ＋（-？_x）~α）u（t, x） = g（t, x） in L^p（R_＋^（1＋n）） subject to the initial temperature u（0, x） = f（x） in L^p（R^n）.
基金
supported by National Natural Science Foundation of China (Grant Nos. 11301249 and 11271175)
the Applied Mathematics Enhancement Program of Linyi University (Grant No. LYDX2013BS059)
Natural Sciences and Engineering Research Council of Canada (FOAPAL) (Grant No. 202979463102000)
关键词
温度场
分数
追踪
初始温度
热方程
弱解
fractional temperature field capacity maximal function
