By Jan Prüss

ISBN-10: 3034804989

ISBN-13: 9783034804981

This ebook offers with evolutionary platforms whose equation of nation may be formulated as a linear Volterra equation in a Banach area. the most function of the kernels concerned is they include unbounded linear operators. the purpose is a coherent presentation of the nation of artwork of the speculation together with unique proofs and its purposes to difficulties from mathematical physics, similar to viscoelasticity, warmth conduction, and electrodynamics with reminiscence. the significance of evolutionary necessary equations ‒ which shape a bigger classification than do evolution equations ‒ stems from such purposes and hence distinctive emphasis is put on those. a few versions are derived and, by way of the built thought, mentioned completely. An annotated bibliography containing 450 entries raises the book’s worth as an incisive reference textual content. --- this wonderful e-book provides a normal method of linear evolutionary platforms, with an emphasis on infinite-dimensional structures with time delays, comparable to these taking place in linear viscoelasticity without or with thermal results. It provides a truly typical and mature extension of the standard semigroup method of a extra common type of infinite-dimensional evolutionary platforms. this can be the 1st visual appeal within the kind of a monograph of this lately constructed conception. a considerable a part of the consequences are as a result of the writer, or are even new. (…) it isn't a e-book that one reads in a number of days. fairly, it may be regarded as an funding with lasting price. (Zentralblatt MATH) during this e-book, the writer, who has been on the leading edge of study on those difficulties for the decade, has amassed, and in lots of areas prolonged, the identified concept for those equations. furthermore, he has supplied a framework that enables one to narrate and evaluation varied ends up in the literature. (Mathematical reports) This ebook constitutes a hugely precious addition to the present literature at the thought of Volterra (evolutionary) quintessential equations and their purposes in physics and engineering. (…) and for the 1st time the tension is at the infinite-dimensional case. (SIAM Reviews)

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