{"product_id":"the-cauchy-problem-for-non-lipschitz-semi-linear-parabolic-partial-differential-equations-9781107477391","title":"The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations","description":"\u003cp\u003e • Author(s): J. C. Meyer | D. J. Needham\u003cbr\u003e • Publisher: Cambridge University Press\u003cbr\u003e • Publisher Imprint: Cambridge University Press\u003cbr\u003e • BISAC: Differential Equations - Partial\u003c\/p\u003e\u003cp\u003eReaction-diffusion theory is a topic which has developed rapidly over the last thirty years, particularly with regards to applications in chemistry and life sciences. Of particular importance is the analysis of semi-linear parabolic PDEs. This monograph provides a general approach to the study of semi-linear parabolic equations when the nonlinearity, while failing to be Lipschitz continuous, is Hölder and\/or upper Lipschitz continuous, a scenario that is not well studied, despite occurring often in models. The text presents new existence, uniqueness and continuous dependence results, leading to global and uniformly global well-posedness results (in the sense of Hadamard). Extensions of classical maximum\/minimum principles, comparison theorems and derivative (Schauder-type) estimates are developed and employed. Detailed specific applications are presented in the later stages of the monograph. Requiring only a solid background in real analysis, this book is suitable for researchers in all areas of study involving semi-linear parabolic PDEs.\u003c\/p\u003e","brand":"Atlantic Books","offers":[{"title":"Paperback","offer_id":46505093005463,"sku":"9781107477391","price":7235.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9781107477391.webp?v=1769193041","url":"https:\/\/atlanticbooks.com\/products\/the-cauchy-problem-for-non-lipschitz-semi-linear-parabolic-partial-differential-equations-9781107477391","provider":"Atlantic Books","version":"1.0","type":"link"}