{"product_id":"asymptotic-behavior-of-scalar-convection-diffusion-equations","title":"Asymptotic Behavior of Scalar Convection-Diffusion Equations","description":"Scalar convection–diffusion equations sit at the crossroads of two fundamental mechanisms: diffusion, which spreads mass, and convection, which transports it. A central question, both mathematically and in applications, is what remains of a solution after a long time, once the transient details of the initial state have vanished. This monograph develops a unified, rigorous theory of large-time asymptotics for scalar convection–diffusion equations in the whole space, with a particular focus on the roles of mass conservation, dimension, and the structure of the nonlinear convective flux. A guiding theme is the emergence of self-similar dynamics: special profiles that encode the scaling invariances of the model and describe the dominant long-time behavior for broad classes of initial data. Depending on the balance between convection and diffusion, three distinct regimes arise, namely, weakly nonlinear, critical self-similar, and strongly nonlinear, each characterized by a different effective asymptotic model and source-type solutions. Originating from lecture notes of a research course and substantially revised and updated, the book combines detailed proofs with a course-friendly presentation. It is designed for graduate students and researchers in analysis and PDEs, and is suitable for use in a Master’s or PhD course, assuming prior familiarity with basic functional analysis and partial differential equations. ","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":58455286513999,"sku":"9783032249739","price":153.95,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0061\/0372\/8217\/files\/9783032249739_1-asymptotic-behavior-of-scalar-convection-diffusion-equations.jpg?v=1786516077","url":"https:\/\/www.suomalainen.com\/products\/asymptotic-behavior-of-scalar-convection-diffusion-equations","provider":"Suomalainen.com","version":"1.0","type":"link"}