Laurie Cossey
Global Media | 2009 | ISBN: 9380168330 | 200 pages | PDF | 1,4 MB
A quick classification of various mathematical problems encountered in the modelization of physical phenomena is proposed in the present chapter. More precisely, the problems considered in this chapter are those that can be reduced to the finding of the solution of a partial differential equation (PDE). Indeed, for many physicists, to pre a model of a phenomenon means to pre a PDE describing this phenomenon. They can be boundary problems, spectral problems, evolution problems. General ideas about the methods of exact and approximate solving of those PDE is also proposed\footnote{The reader is supposed to have a good knowledge of the solving of ordinary differential equations. A good reference on this subject is ).}. This chapter contains numerous references to the "physical" part of this book which justify the interest given to those mathematical problems. In classical books about PDE, equations are usually classified into three categories:
hyperbolic, parabolic and elliptic equation. This classification is connected to the proof of existence and unicity of the solutions rather than to the actual way of obtaining the solution. We present here another classification connected to the way one obtains the solutions: we distinguish mainly boundary problems and evolution problems.
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