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Existenzsätze mit der linienmethode für parabolische probleme und periodische lösungen von ut=f(t,x,u,ux,uxx)

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Abstract

The (longitudinal) method of lines transforms a parabolic equation into a first order system of ordinary differential equations by discretization of the spatial variable. It is shown how to obtain existence theorems for nonlinear parabolic equations from those for ordinary differential equations under general growth conditions and weak regularity assumptions. The method is demonstrated in proving a new existence theorem for periodic solutions to ut=f(t,x,u,ux,uxx) with boundary conditions of Dirichlet type.

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  1. Mathematisches Institut I, Universität Karlsruhe, englerstraße 2, D-7500, Karlsruhe 1

    Jörg Heuß

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  1. Jörg Heuß
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Heuß, J. Existenzsätze mit der linienmethode für parabolische probleme und periodische lösungen von ut=f(t,x,u,ux,uxx). Manuscripta Math 30, 137–162 (1979). https://doi.org/10.1007/BF01300966

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  • DOI: https://doi.org/10.1007/BF01300966

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