Partial Differential Equations in Action: From Modelling to Theory 4th ed. 2022 Edition
暫譯: 偏微分方程的應用：從建模到理論（第4版，2022年版）
Salsa, Sandro, Verzini, Gianmaria
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商品描述
This work is an updated version of a book evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background for numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In the second part, chapters 6 to 10 concentrate on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems, while Chapter 11 deals with vector-valued conservation laws, extending the theory developed in Chapter 4. The main differences with respect to the previous editions are: a new section on reaction diffusion models for population dynamics in a heterogeneous environment; several new exercises in almost all chapters; a general restyling and a reordering of the last chapters. The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering.
商品描述(中文翻譯)
這本書是從米蘭理工大學（Politecnico di Milano）過去幾年所開設的偏微分方程（PDEs）課程演變而來的更新版本。這些課程有兩個主要目的：一方面教導學生欣賞理論與應用科學中出現的問題之間的互動，另一方面則是為他們提供數值方法（如有限元素法）的堅實理論基礎。因此，本教科書分為兩個部分。第一部分，即第2至第5章，性質較為基礎，專注於發展和研究來自擴散、傳播和運輸、波動與振動等宏觀領域的基本問題。第二部分，即第6至第10章，則集中於希爾伯特空間方法的發展，用於變分形式的分析（主要是）線性邊界和初邊界值問題，而第11章則處理向量值的守恆定律，擴展了第4章中發展的理論。與之前版本的主要差異包括：新增一節關於異質環境中人口動態的反應擴散模型；幾乎所有章節中都有若干新的練習題；以及對最後幾章進行了全面的重新設計和排序。本書旨在作為高級本科或第一年研究生課程，適合來自應用數學、物理學和工程等各個學科的學生。
作者簡介
Sandro Salsa is a Emeritus Professor of Mathematical Analysis at Politecnico of Milan, where he has been one of the main founders of the educational program in Mathematical Engineering. His research interest ranges over diverse aspects of nonlinear, nonlocal, singular or degenerate elliptic and parabolic equations, with particular emphasis on boundary behavior, regularity and free boundary problems. He is an author of 14 books and several papers in the most prestigious scientific mathematical journals.
Gianmaria Verzini is a Professor of Mathematical Analysis at the Department of Mathematics of the Politecnico of Milan. He is author of 5 books and more than 50 papers, published on prominent international journals. His scientific interests concern the applications of Nonlinear Analysis to the existence, multiplicity, qualitative properties and regularity of solutions to nonlinear differential equations and systems.
作者簡介(中文翻譯)
Sandro Salsa 是米蘭理工學院數學分析的名譽教授，他是數學工程教育計畫的主要創始人之一。他的研究興趣涵蓋非線性、非局部、奇異或退化的橢圓和拋物方程的多個方面，特別強調邊界行為、正則性和自由邊界問題。他是14本書籍的作者，以及在最具聲望的科學數學期刊上發表的多篇論文。
Gianmaria Verzini 是米蘭理工學院數學系的數學分析教授。他是5本書籍的作者，並在知名國際期刊上發表了超過50篇論文。他的科學興趣涉及非線性分析在非線性微分方程及系統的存在性、多重性、質量特性和正則性方面的應用。
