Selected Papers I

• Partial Differential Equations.- On the existence of Green’s Function.- Parabolic Equations.- On Cauchy’s Problem for Hyperbolic Equations and the Differentiability of Solutions of Elliptic Equations.- The Propagation of Discontinuities in Wave Motion.- Asymptotic Solutions of Oscillatory Initial Value Problems.- Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations.- On Stability for Difference Schemes; a Sharp Form of Gårding’s Inequality.- An Example of Huygens’ Principle.- A Simple One-dimensional Model for the Three-dimensional Vorticity Equation.- Commentary on Part I.- Difference Approximations to PDE.- Survey of the Stability of Linear Finite Difference Equations.- On the Stability of Difference Approximations to Solutions of Hyperbolic Equations With Variable Coefficients.- The Computation of Discontinuous Solutions of Linear Hyperbolic Equations.- Accuracy and Resolution in the Computation of Solutions of Linear and Nonlinear Equations.- Commentary on Part II.- Hyperbolic Systems of Conservation Laws.- Weak Solutions of Nonlinear Hyperbolic Equations and Their Numerical Computation.- Hyperbolic Systems of Conservation Laws II.- Systems of Conservation Laws.- Difference Schemes for Hyperbolic Equations with High Order of Accuracy.- Shock Waves and Entropy.- Systems of Conservation Equations with a Convex Extension.- Positive Schemes for Solving Multi-Dimensional Hyperbolic Systems of Conservation Laws.- Commentary on Part III.- Integrable Systems.- Integrals of Nonlinear Equations of Evolution and Solitary Waves.- Periodic Solutions of the KdV Equation.- Almost Periodic Solutions of the KdV Equation.- The Small Dispersion Limit of the Korteweg-de Vries Equation. I.- The Small Dispersion Limit of the Korteweg-de Vries Equation. II.- The Small Dispersion Limit of the Korteweg-deVries Equation. III.- On Dispersive Difference Schemes. I.- Dispersive Approximations in Fluid Dynamics.- Commentary on Part IV.

From the reviews: "This is a collection of papers by one of the great mathematicians of our time. ... The depth and wide range covered by Lax's research contributions illustrate his broad view of mathematical analysis as a whole. The editors ... have done an excellent job: they didn't just collect some papers 'at random', but also explain, in detailed commentaries, the contents and importance of the included publications at the end of each section." (Jurgen Appell, Zentralblatt MATH, Vol. 1087, 2006) "Since Peter Lax was chosen as the recipient of the 2005 Abel Prize, it's hardly necessary to say that his work is important. Libraries should consider his Selected Papers an essential acquisition. This first volume collects papers on partial differential equations, difference equations approximating PDEs, hyperbolic systems of conservation laws, and integrable systems." (Fernando Q. Gouvea, MathDL, October, 2005)