Cauchy Problems and Evolution Operators
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Any theory of abstract quasilinear parabolic problems requires, of course, a good understanding of the theory of linear parabolic evolution equations. In this chapter we develop that part of the linear theory which is based upon the concept of evolution operators. The latter correspond to the fundamental matrices in the theory of ordinary differential equations. This ‘classical’ theory is particularly well-suited for the study of quasilinear parabolic problems exhibiting smoothing phenomena since it exploits the fact that the solution of a linear parabolic evolution equation has in general better regularity properties than its initial value.
KeywordsCauchy Problem Evolution Operator Mild Solution Nonempty Closed Convex Subset Closed Convex Cone
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