Much progress has been made in recent years on the issue of asymptotic behavior of problems set in cylinders. This book goes one step further by presenting the latest accomplishments on asymptotic behavior in domains which become unbounded.It also investigates new issues which have emerged including existence and uniqueness of solution in unbounded domains, anisotropic singular perturbations, periodic behavior forced by periodic data. These new advances are treated with original techniques developed to investigate the asymptotic behavior of various problems.Theories investigated throughout the book can be applied to other problems related to partial differential equations, making it an important text for students and researchers within the discipline.Asymptotic Issues for Some Partial Differential Equations is an updated account of Goes to Plus Infinity, published by Birkhäuser in 2002.