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Partial Differential Equations and Applications: A Bridge for Students and Researchers in Applied Sciences offers a unique approach to this key subject by connecting mathematical principles to the latest research advances in select topics. Beginning with very elementary PDEs, such as classical heat equations, wave equations and Laplace equations, the book focuses on concrete examples. It gives students basic skills and techniques to find explicit solutions for partial differential equations.As it progresses, the book covers more advanced topics such as the maximum principle and applications, Green's representation, Schauder's theory, finite-time blowup, and shock waves. By exploring these topics, students gain the necessary tools to deal with research topics in their own fields, whether proceeding in math or engineering areas.Class tested over multiple years with advanced undergraduate and graduate coursesFeatures many concrete examples and chapter exercisesAppropriate for advanced undergraduate and graduate courses geared to math and engineering studentsRequires minimal background beyond advanced calculus and differential equations

Differential Equations, Partial --- Difference Equations --- Mathematics --- Differential equations, Partial.

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The book could be a good companion for any graduate student in partial differential equations or in applied mathematics. Each chapter brings indeed new ideas and new techniques which can be used in these fields. The differents chapters can be read independently and are of great pedagogical value. The advanced researcher will find along the book the most recent achievements in various fields.·Independent chapters·Most recent advances in each fields·Hight didactic quality ·Self contained·Excellence of the contributors·Wide range of topics

Differential equations --- Differential equations, Partial

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Differential equations and applications

Differential equations, Partial --- Differential equations, Nonlinear

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A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations have been the solitons, shock waves and turbulence or chaotical processes. In many ways, these phenomen

Differential equations, Partial. --- Differential equations, Nonlinear.

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In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Differential equations, Nonlinear. --- Differential equations, Partial. --- Partial differential equations --- Nonlinear differential equations --- Nonlinear theories --- Differential equations, Partial --- Differential equations, Nonlinear