{"product_id":"pseudo-monotone-operator-theory-for-unsteady-alex-kaltenbach-9783031296697","title":"Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents","description":"This book provides a comprehensive analysis of the existence of weak solutions of unsteady problems with variable exponents. The central motivation is the weak solvability of the unsteady p(., .)-Navier-Stokes equations describing the motion of an incompressible electro-rheological fluid. Due to the variable dependence of the power-law index p(., .) in this system, the classical weak existence analysis based on the pseudo-monotone operator theory in the framework of Bochner-Lebesgue spaces is not applicable. As a substitute for Bochner-Lebesgue spaces, variable Bochner-Lebesgue spaces are introduced and analyzed. In the mathematical framework of this substitute, the theory of pseudo-monotone operators is extended to unsteady problems with variable exponents, leading to the weak solvability of the unsteady p(., .)-Navier-Stokes equations under general assumptions.\u003cp\u003eAimed primarily at graduate readers, the book develops the material step-by-step, starting with the basics of PDE theory and non-linear functional analysis. The concise introductions at the beginning of each chapter, together with illustrative examples, graphics, detailed derivations of all results and a short summary of the functional analytic prerequisites, will ease newcomers into the subject.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Alex Kaltenbach\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3031296699\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783031296697\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 08\/12\/2023\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 358\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.15lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.77d\u003c\/p\u003e","brand":"Alex Kaltenbach","offers":[{"title":"Paperback","offer_id":45477005328639,"sku":"9783031296697","price":64.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_d0b24403-a032-40ae-aeb9-8b82b16a787a.jpg?v=1715918786","url":"https:\/\/www.whiterainbookhouse.com\/products\/pseudo-monotone-operator-theory-for-unsteady-alex-kaltenbach-9783031296697","provider":"WR Book House","version":"1.0","type":"link"}