{"product_id":"abstract-parabolic-evolution-equations-and-atsushi-yagi-9789811618956","title":"Abstract Parabolic Evolution Equations and Lojasiewicz-Simon Inequality I: Abstract Theory","description":"The classical Lojasiewicz gradient inequality (1963) was extended by Simon (1983) to the infinite-dimensional setting, now called the Lojasiewicz-Simon gradient inequality. This book presents a unified method to show asymptotic convergence of solutions to a stationary solution for abstract parabolic evolution equations of the gradient form by utilizing this Lojasiewicz-Simon gradient inequality.\u003cbr\u003eIn order to apply the abstract results to a wider class of concrete nonlinear parabolic equations, the usual Lojasiewicz-Simon inequality is extended, which is published here for the first time. In the second version, these abstract results are applied to reaction-diffusion equations with discontinuous coefficients, reaction-diffusion systems, and epitaxial growth equations. The results are also applied to the famous chemotaxis model, i.e., the Keller-Segel equations even for higher-dimensional ones.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Atsushi Yagi\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 981161895X\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9789811618956\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 06\/01\/2021\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 61\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.25lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.15d","brand":"Atsushi Yagi","offers":[{"title":"Paperback","offer_id":44302403535103,"sku":"9789811618956","price":69.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_991bc413-dc8c-4102-b025-cb6e2f4ffee0.jpg?v=1695161367","url":"https:\/\/www.whiterainbookhouse.com\/products\/abstract-parabolic-evolution-equations-and-atsushi-yagi-9789811618956","provider":"WR Book House","version":"1.0","type":"link"}