{"title":"Yoshikazu Giga","description":null,"products":[{"product_id":"basic-guide-to-uniqueness-problems-for-evolutionary-differential-equations-book-mi-ho-giga-9783031347955","title":"A Basic Guide to Uniqueness Problems for Evolutionary Differential Equations","description":"This book addresses the issue of uniqueness of a solution to a problem – a very important topic in science and technology, particularly in the field of partial differential equations, where uniqueness guarantees that certain partial differential equations are sufficient to model a given phenomenon.   This book is intended to be a short introduction to uniqueness questions for initial value problems. One often weakens the notion of a solution to include non-differentiable solutions. Such a solution is called a weak solution. It is easier to find a weak solution, but it is more difficult to establish its uniqueness. This book examines three very fundamental equations: ordinary differential equations, scalar conservation laws, and Hamilton-Jacobi equations. Starting from the standard Gronwall inequality, this book discusses less regular ordinary differential equations. It includes an introduction of advanced topics like the theory of maximal monotone operators as wellas what is called DiPerna-Lions theory, which is still an active research area. For conservation laws, the uniqueness of entropy solution, a special (discontinuous) weak solution is explained. For Hamilton-Jacobi equations, several uniqueness results are established for a viscosity solution, a kind of a non-differentiable weak solution. The uniqueness of discontinuous viscosity solution is also discussed. A detailed proof is given for each uniqueness statement.      The reader is expected to learn various fundamental ideas and techniques in mathematical analysis for partial differential equations by establishing uniqueness. No prerequisite other than simple calculus and linear algebra is necessary. For the reader’s convenience, a list of basic terminology is given at the end of this book.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":50096776282385,"sku":"NGR9783031347955","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52126738514193,"sku":"NLS9783031347955","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3031347951.jpg?v=1751252473"},{"product_id":"surface-evolution-equations-book-yoshikazu-giga-9783764324308","title":"Surface Evolution Equations","description":"This book is intended to be a self-contained introduction to analytic foundations of a level set method for various surface evolution equations including curvature ?ow equations. These equations are important in various ?elds including material sciences, image processing and di?erential geometry. The goal of this book is to introduce a generalized notion of solutions allowing singularities and solve the initial-value problem globally-in-time in a generalized sense. Various equivalent de?nitions of solutions are studied. Several new results on equivalence are also presented. Wepresentherearathercompleteintroductiontothetheoryofviscosityso- tionswhichis a keytoolforthe levelsetmethod. Alsoa self-containedexplanation isgivenforgeneralsurfaceevolutionequationsofthe secondorder.Althoughmost ofthe resultsin this book aremoreor lessknown,they arescatteredinseveralr- erences, sometimes without proof. This book presents these results in a synthetic way with full proofs. However, the references are not exhaustive at all. The book is suitable for applied researchers who would like to know the detail of the theory as well as its ?avour.No familiarity with di?erential geometry and the theory of viscosity solutions is required. The prerequisites are calculus, linear algebra and some familiarity with semicontinuous functions. This book is also suitable for upper level under graduate students who are interested in the ?eld.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51061456961809,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51061459681553,"sku":"NIN9783764324308","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3764324309.jpg?v=1751221460"},{"product_id":"what-mathematics-can-do-for-you-book-yoshikazu-giga-9784431546818","title":"What Mathematics Can Do for You","description":"This book covers topics ranging from mathematical problems in specific areas to mathematical strategy that helps a leader who must weigh many issues and make timely decisions, to the ways that mathematical literacy helps ensure quality control.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52146696913169,"sku":"NLS9784431546818","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9784431546818.jpg?v=1757598276"},{"product_id":"role-of-metrics-in-the-theory-of-partial-differential-the-proceedings-of-the-11t-book-yoshikazu-giga-9784864970907","title":"Role Of Metrics In The Theory Of Partial Differential, The - Proceedings Of The 11th Mathematical Society Of Japan, Seasonal Institute (Msj-si)","description":"This volume is edited as the proceedings of the 11th Mathematical Society of Japan, Seasonal Institute (MSJ-SI) \"The Role of Metrics in the Theory of Partial Differential Equations\", held for the period of July 2-13, 2018 in Hokkaido University, Sapporo, Japan. This volume consists of peer-reviewed articles written by speakers who actively lead the fields of partial differential equations, numerical analysis, harmonic analysis, and geometric analysis. It should be underlined that 3 survey articles provided by course lecturers show an interesting direction of analysis under various metrics. This volume is suitable for any graduate students and young researchers to motivate the research on these fields from the viewpoint of metrics.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52452709499153,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52452710121745,"sku":"NLS9784864970907","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9784864970907.jpg?v=1759365625"},{"product_id":"what-mathematics-can-do-for-you-book-yoshikazu-giga-9784431543459","title":"What Mathematics Can Do for You","description":"This book covers topics ranging from mathematical problems in specific areas to mathematical strategy that helps a leader who must weigh many issues and make timely decisions, to the ways that mathematical literacy helps ensure quality control.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52676002775313,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52676003496209,"sku":"NLS9784431543459","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9784431543459.jpg?v=1762303251"}],"url":"https:\/\/www.worldofbooks.com\/en-gb\/collections\/author-books-by-yoshikazu-giga.oembed","provider":"World of Books ","version":"1.0","type":"link"}