<< 1 >>
Rating: 
Summary: Difficult topics treated in a comprehensive manner.
Review: One of the most important and subtle features of mathematics is the great difference existing between linearity and non-linearity. One always tries to linearize whenever possible, because linear problems are easier to solve, but unfortunately the world is not linear, and we have to learn how to deal with non-linear problems.This volume discusses thoroughly some very important cases of non-linear PDE's which are important in mathematical physics or that possess intrinsic theoretical interest. The contents are: Function space and operator theory for nonlinear analysis; nonlinear elliptic equations; nonlinear parabolic equations; nonlinear hyperbolic equations; Euler and Navier-Stokes equations for incompressible fluids; Einstein's equations. A little bit more advanced and speciallized than the other two volumes, but still useful for a broad community. A graduate student with a solid background will find it perfectly acquaintable. Includes lots of excercises and references. Please read my other reviews (just click on my name above).
Rating: 
Summary: Navier-Stokes, and Einstein's eqtn
Review: This final volume, of a set of three, discusses what *little* is generally known about the extraordinarily diverse set of non-linear PDE. The first chapter of the text presents function spaces and operator theory for non-linear analysis. That chapter presents a number of analytical techniques including L^p sobolev spaces, imbedding theorems, Holder and Zygmund spaces, pseudo and para differential operators and more. Three following chapters discuss nonlinear elliptic, parabolic and hyperbolic PDE. Those chapters present many interesting results such as the Nash imbedding theorem, minimal surfaces, Nash -Moser inequalities, fixed point theorems, non-linear Trotter products, quasi-linear parabolic and hyperbolic, compressible fluids, Cauchy -Kowalewski theorem,. Riemann invariants and entropy flux, and strings. The final two chapters cover incompressible fluids and Einstein's equations. Both chapters are ideal for physicists in need of a reference detailing rigorous existence proofs, and formulations. As with other volumes in this seriers, the writing in this text is for the professional mathematician or advanced graduate student. Having said that, these volumes make an ideal set for someone who seeks to have a definitive and up to date account of what is known about PDE in general
Rating:
Summary: Navier-Stokes, and Einstein's eqtn
Review: This final volume, of a set of three, discusses what *little* is generally known about the extraordinarily diverse set of non-linear PDE. The first chapter of the text presents function spaces and operator theory for non-linear analysis. That chapter presents a number of analytical techniques including L^p sobolev spaces, imbedding theorems, Holder and Zygmund spaces, pseudo and para differential operators and more. Three following chapters discuss nonlinear elliptic, parabolic and hyperbolic PDE. Those chapters present many interesting results such as the Nash imbedding theorem, minimal surfaces, Nash -Moser inequalities, fixed point theorems, non-linear Trotter products, quasi-linear parabolic and hyperbolic, compressible fluids, Cauchy -Kowalewski theorem,. Riemann invariants and entropy flux, and strings. The final two chapters cover incompressible fluids and Einstein's equations. Both chapters are ideal for physicists in need of a reference detailing rigorous existence proofs, and formulations. As with other volumes in this seriers, the writing in this text is for the professional mathematician or advanced graduate student. Having said that, these volumes make an ideal set for someone who seeks to have a definitive and up to date account of what is known about PDE in general
<< 1 >>
| 
