This paper proves that if the kernel k (x) is mildly singular, that is to say, (△) k ∈ Lp ( Rn) for p ∈( n/α-1 , +∞] , or the initial date u0≥0 satisfies u0 ∈ L1 (Rn), and the kernel k (x) is strongly singular, that is to say, (△)k ∈LP，∞ (Rn) for P∈ (1, n/α-1], and the initial date u0 satisfies ‖ u0‖q* ＜ε for q* =n/n+a-1-n/p ∈[1,n/a-1), the global well - posedness of the Cauchy problem for diffusive aggregation equations is obtained.%证明了如果核函数是弱奇性的,即▽k∈Lp(Rn),p∈(n/α-1,+∞),非负初值u0满足u0∈L1(Rn);或者核函数是强奇性的即▽k∈Lp,∞(Rn),p∈(1,n/α-1),初值u0满足‖u0‖q*＜ε,其中q*=n/n+α-1-n/p∈[1,n/α-1],那么耗散型聚合方程组的Cauchy问题是整体适定的.
展开▼
