Distributions in the physical and engineering sciences. Volume 2: Linear and nonlinear dynamics in continuous media
This book follows [Volume 1 (1977; Zbl 0880.46028)] as the second of a series of three volumes. The present volume, ``Linear and nonlinear dynamics in continuous media'', contains Part III, ``Potentials, diffusions, and waves'' and Part IV, ``Nonlinear partial differential equations''. Part III consists of three chapters: Potential theory and fundamental solutions of elliptic equations; Diffusion and parabolic evolution equations; Waves and hyperbolic equations. Part IV is divided into four chapters: First-order nonlinear PDEs and conservation laws; Generalized solutions of first-order nonlinear PDEs; Nonlinear waves and growing interfaces: 1-D Burgers and Kardar-Parisi-Zhang models. Many exercises are proposed at the end of each chapter. The authors point out that many of them are really small research projects. Solutions to all of them are included in Appendix A. The book will be useful to graduate students and researchers who are interested in the applications of distributions and partial differential equations to the applied sciences.
nonlinear partial differential equations
scientific article; zbMATH DE number 6162126