This book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. Researchers and graduate students in applied mathematics and engineering will find Initial-Boundary Value Problems and the Navier-Stokes Equations invaluable. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. There are many new results, in particular on the Navier-Stokes equations. The direct approach to the subject still gives a valuable introduction to an important area of applied analysis.
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Book Description
Initial-Boundary Value Problems and the Navier-Stokes Equations gives an introduction to the vast subject of initial and initial-boundary value problems for PDEs. Researchers and graduate students in applied mathematics and engineering will find Initial-Boundary Value Problems and the Navier-Stokes Equations invaluable.
--This text refers to the
Paperback
edition.
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0 of 7 people found the following review helpful:
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Runge-Kutta method for Navier-Stokes Equation,
By Surya Prasad A (Kerala, India) - See all my reviews
This review is from: Initial-boundary value problems and the Navier-Stokes equations, Volume 136 (Pure and Applied Mathematics) (Hardcover)
Solving the Compressible two dimensional NAvier-Stokes Equationusing Fourth order Runge-Kutta method
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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one space dimension, matrix theorem, transport theorem, local existence theorem, spatially periodic case, basic energy estimate, strongly hyperbolic system, strip problem, strong hyperbolicity, ordinary initial value problem, several space dimensions, resolvent condition, unique smooth solution, incompressible equations, symmetric hyperbolic systems, parabolic systems, basic estimate Key Phrases - Capitalized Phrases (CAPs): (learn more)
Initial-Boundary Value Problems, Constant-Coefficient Cauchy Problems, Nonlinear Example, The Incompressible Navier-Stokes Equations, Linear Variable-Coefficient Cauchy Problems, Several Dimensions, The Spatially Periodic Case, Nonlinear Systems, Gronwall's Lemma, Picard's Lemma, Using the Sobolev, Example Continued Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
one space dimension, matrix theorem, transport theorem, local existence theorem, spatially periodic case, basic energy estimate, strongly hyperbolic system, strip problem, strong hyperbolicity, ordinary initial value problem, several space dimensions, resolvent condition, unique smooth solution, incompressible equations, symmetric hyperbolic systems, parabolic systems, basic estimate Key Phrases - Capitalized Phrases (CAPs): (learn more)
Initial-Boundary Value Problems, Constant-Coefficient Cauchy Problems, Nonlinear Example, The Incompressible Navier-Stokes Equations, Linear Variable-Coefficient Cauchy Problems, Several Dimensions, The Spatially Periodic Case, Nonlinear Systems, Gronwall's Lemma, Picard's Lemma, Using the Sobolev, Example Continued Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
22
books
cite this book:
See all 22 books citing this book
- An Introduction to Nonlinear Partial Differential Equations by J. David Logan on page 49, and page 182
- Incompressible Flow and the Finite Element Method, Volume 1, Advection-Diffusion and Isothermal Laminar Flow by P. M. Gresho in Back Matter
- Asymptotic Modelling of Fluid Flow Phenomena (Fluid Mechanics and Its Applications, Volume 64) by Radyadour Zeytounian in Back Matter
- Nonlinear Partial Differential Equations for Scientists and Engineers, Second Edition by Lokenath Debnath in Back Matter
- Hyberbolic Problems: Theory, Numerics, Applications: Seventh International Conference on Hyberbolic Problems (International Series of Numerical Mathematics) by Rolf Jeltsch on page 271
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