By Yuxi Zheng

ISBN-10: 0817640800

ISBN-13: 9780817640804

ISBN-10: 1461266319

ISBN-13: 9781461266310

This paintings is predicated at the lecture notes of the direction M742: issues in Partial Dif ferential Equations, which I taught within the Spring semester of 1997 at Indiana Univer sity. My major purpose during this direction was once to offer a concise advent to fixing two-dimensional compressibleEuler equations with Riemann facts, that are specific Cauchy info. This publication covers new theoretical advancements within the box during the last decade or so. priceless wisdom of one-dimensional Riemann difficulties is reviewed and a few popularnumerical schemes are awarded. Multi-dimensional conservation legislation are extra actual and the time has come to check them. the speculation onbasicone-dimensional conservation legislation isfairly whole offering sturdy starting place for multi-dimensional difficulties. the wealthy thought on ellip tic and parabolic partial differential equations has nice strength in functions to multi-dimensional conservation legislation. And swifter pcs make itpossible to bare numerically extra info for theoretical pursuitin multi-dimensional difficulties. assessment and highlights bankruptcy 1is an outline ofthe concerns that trouble us inthisbook. It lists theEulersystemandrelatedmodelssuch as theunsteady transonic small disturbance, pressure-gradient, and pressureless structures. Itdescribes Mach re flection and the von Neumann paradox. In Chapters 2-4, which shape half I of the ebook, we in brief current the speculation of one-dimensional conservation legislation, which in cludes strategies to the Riemann difficulties for the Euler method and common strictly hyperbolic and surely nonlinearsystems, Glimm's scheme, and large-time asymp toties.

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Systems of Conservation Laws: Two-Dimensional Riemann Problems (Progress in Nonlinear Differential Equations and Their Applications 38) by Yuxi Zheng

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