Год выпуска: 2011 Автор: Huseyin Merdan Издательство: LAP Lambert Academic Publishing Страниц: 72 ISBN: 9783845438276
Описание
This book presents applications of the methods known as renormalization group (RG) and scaling in the physics literature to applied mathematics problems after a brief review of the methodology. The first part involves an application to a class of nonlinear parabolic differential equations. First, RG methods are described for determining the key exponents related to the decay of solutions to these equations. The determination of decay exponents is viewed as an asymptotically self similar process that facilitates an RG approach. The methods are also extended to higher order in the small coefficient of the nonlinearity. Finally, the RG results are verified in some cases by rigorous proofs and other calculations. In the second part, the application of RG technique to systems of equations describing interface problems is presented. The temporal evaluation of an interface separating two phases is analyzed for large time. The standard sharp interface problem in the...
