Nonlinear Partial Differential Equations with Applications
Nonlinear Partial Differential Equations with Applications

Author: Tomás Roubicek

Publisher: Springer Science & Business Media

Published: 2006-01-17

Total Pages: 415

ISBN-13: 3764373970

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This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.

A Stability Technique for Evolution Partial Differential Equations
A Stability Technique for Evolution Partial Differential Equations

Author: Victor A. Galaktionov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 388

ISBN-13: 1461220505

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* Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations. * Written by established mathematicians at the forefront of their field, this blend of delicate analysis and broad application is ideal for a course or seminar in asymptotic analysis and nonlinear PDEs. * Well-organized text with detailed index and bibliography, suitable as a course text or reference volume.

Numerical Methods for Nonlinear Partial Differential Equations
Numerical Methods for Nonlinear Partial Differential Equations

Author: Sören Bartels

Publisher: Springer

Published: 2015-01-19

Total Pages: 394

ISBN-13: 3319137972

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The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.

Nonlinear Partial Differential Equations
Nonlinear Partial Differential Equations

Author: Mi-Ho Giga

Publisher: Springer Science & Business Media

Published: 2010-05-30

Total Pages: 307

ISBN-13: 0817646515

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This work will serve as an excellent first course in modern analysis. The main focus is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. This textbook will be an excellent resource for self-study or classroom use.

Nonlinear Partial Differential Equations for Future Applications
Nonlinear Partial Differential Equations for Future Applications

Author: Shigeaki Koike

Publisher: Springer

Published: 2022-04-17

Total Pages: 261

ISBN-13: 9789813348240

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This volume features selected, original, and peer-reviewed papers on topics from a series of workshops on Nonlinear Partial Differential Equations for Future Applications that were held in 2017 at Tohoku University in Japan. The contributions address an abstract maximal regularity with applications to parabolic equations, stability, and bifurcation for viscous compressible Navier–Stokes equations, new estimates for a compressible Gross–Pitaevskii–Navier–Stokes system, singular limits for the Keller–Segel system in critical spaces, the dynamic programming principle for stochastic optimal control, two kinds of regularity machineries for elliptic obstacle problems, and new insight on topology of nodal sets of high-energy eigenfunctions of the Laplacian. This book aims to exhibit various theories and methods that appear in the study of nonlinear partial differential equations.

Weak and Measure-Valued Solutions to Evolutionary PDEs
Weak and Measure-Valued Solutions to Evolutionary PDEs

Author: J. Malek

Publisher: CRC Press

Published: 2019-08-16

Total Pages: 334

ISBN-13: 1000723127

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This book provides a concise treatment of the theory of nonlinear evolutionary partial differential equations. It provides a rigorous analysis of non-Newtonian fluids, and outlines its results for applications in physics, biology, and mechanical engineering.

Nonlinear Partial Differential Equations for Scientists and Engineers
Nonlinear Partial Differential Equations for Scientists and Engineers

Author: Lokenath Debnath

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 602

ISBN-13: 1489928464

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This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from diverse fields. Methods and properties of solutions, along with their physical significance, help make the book more useful for a diverse readership. The book is an exceptionally complete text/reference for graduates, researchers, and professionals in mathematics, physics, and engineering.

Beyond Partial Differential Equations
Beyond Partial Differential Equations

Author: Horst Reinhard Beyer

Publisher: Springer

Published: 2007-04-10

Total Pages: 291

ISBN-13: 3540711295

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This book introduces the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis, with only some examples requiring more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Emphasis is placed on equations of the hyperbolic type which are less often treated in the literature.

New Tools for Nonlinear PDEs and Application
New Tools for Nonlinear PDEs and Application

Author: Marcello D'Abbicco

Publisher: Springer

Published: 2019-05-07

Total Pages: 392

ISBN-13: 3030109372

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This book features a collection of papers devoted to recent results in nonlinear partial differential equations and applications. It presents an excellent source of information on the state-of-the-art, new methods, and trends in this topic and related areas. Most of the contributors presented their work during the sessions "Recent progress in evolution equations" and "Nonlinear PDEs" at the 12th ISAAC congress held in 2017 in Växjö, Sweden. Even if inspired by this event, this book is not merely a collection of proceedings, but a stand-alone project gathering original contributions from active researchers on the latest trends in nonlinear evolution PDEs.