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The semigroup approach to first order quasilinear equations in several space variables

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Abstract

The Cauchy problem for u t + Σ ni = 1 (φ i (u)) xi = 0 is treated via the theory of semigroups of nonlinear transformations. This treatment requires the development of results concerning the time-independent equation u + Σ ni = 1 (φ i (u)) xi = h for h∈L 1(Rn), which in turn is studied via the regularized equation

$$ u + \sum\nolimits_{i = 1}^n {\left( {\phi _i \left( u \right)} \right)} _{xi} - \varepsilon \Delta u = h $$

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Authors and Affiliations

  1. Mathematics Research Center, University of Wisconsin, Wisconsin, USA

    Michael G. Crandall

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  1. Michael G. Crandall
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Sponsored by the United States Army under Contract No.: DA-31-124-ARO-D-462.

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Crandall, M.G. The semigroup approach to first order quasilinear equations in several space variables. Israel J. Math. 12, 108–132 (1972). https://doi.org/10.1007/BF02764657

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  • DOI: https://doi.org/10.1007/BF02764657

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