Geometric-Qualitative Approach

Inna Shingareva () and Carlos Lizárraga-Celaya ()
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Inna Shingareva: University of Sonora, Department of Mathematics
Carlos Lizárraga-Celaya: University of Sonora, Department of Physics

Chapter Chapter 3 in Solving Nonlinear Partial Differential Equations with Maple and Mathematica, 2011, pp 145-186 from Springer

Abstract: Abstract In this chapter, following a geometric-qualitative approach to partial differential equations, we will consider important methods and concepts concerning quasilinear and nonlinear PDEs (in two independent variables) and solutions of classical and generalized Cauchy problems (with continuous and discontinuous initial data), namely, the Lagrange method of characteristics and its generalizations, the concepts of solution surfaces (or integral surfaces), general solutions, discontinuous or weak solutions, solution profiles at infinity, complete integrals, the Monge cone, characteristic directions.

Keywords: Cauchy Problem; Phase Portrait; Travel Wave Solution; Tangent Plane; Gordon Equation (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7091-0517-7_3

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DOI: 10.1007/978-3-7091-0517-7_3

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