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摘要
The solvability of the abstract Cauchy problem for the quasilinear evolution equation u'(t) = A(u(t)) u(t) for t > 0 and u(0) = u(0) is an element of D is discussed. Here {A(w); w is an element of Y} is a family of closed linear operators in a real Banach space X such that Y subset of D (A(w)) subset of (Y) over bar for w is an element of Y, Y is another Banach space which is continuously embedded in X, and D is a closed subset of Y. The existence and uniqueness of C1 solutions to the Cauchy problem is proved without assuming that Y is dense in X or D(A(w)) is independent of w. The abstract result is applied to obtain an L-1-valued C-1-solution to a size-structured population model.
- 出版日期2017-10
