ABSTRACT PARABOLIC EQUATIONS WITH APPLICATIONS TO PROBLEMS IN CYLINDRICAL SPACE DOMAINS

作者：Di Cristo Michele^*; Guidetti Davide; Lorenzi Alfredo

来源：Advances in Differential Equations, 2010, 15(1-2): 1-42.

In a Banach space X we consider the partial differential equation
(*) D(t)u(t,x) + (-1)(m)a(x)D(x)(2m)u(t,x) - A(x)u(t,x) = f(t,x)
where m is a positive integer, related to the rectangle (0, T) x (0, L) and the family of closed linear operators {A(x)}(x is an element of[0,L]). Under suitable assumptions we uniquely solve certain initial and boundary-value problems associated with (*). Some applications are given when, for each x, A(x) is an explicit linear uniformly elliptic differential operator.

• 出版日期2010-2