Article ID Journal Published Year Pages File Type
4610686 Journal of Differential Equations 2014 26 Pages PDF
Abstract

This paper is concerned with the solvability for the Cauchy problem of heat equations in RNRN (N⩾2N⩾2) with singular lower order terms:{∂u∂t(x,t)=Δu(x,t)−βx|x|2⋅∇u(x,t)+c|x|2u(x,t)+f(x,t)in RN×(0,T),u(x,0)=u0(x)in RN, where β∈Rβ∈R, c⩽(N−2−β)2/4c⩽(N−2−β)2/4, u0u0 is an initial value, f   is an inhomogeneous term and T∈(0,∞]T∈(0,∞] is arbitrarily given. In particular, u0u0 and f   are taken from a weighted LpLp-space. The result generalizes the one of Baras and Goldstein (1984) [2] from β=0β=0 to β≠0β≠0 and improves the one of Arendt, Goldstein and Goldstein (2006) [1] which deals with an m  -accretive realization of the linear part in a weighted LpLp-space under the stronger condition c⩽(N−2−β)2(p−1)/p2c⩽(N−2−β)2(p−1)/p2. Moreover, this paper clarifies some regularities of solutions.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
Authors
, , ,