Skip to main content Accessibility help
×
Home

Aspects of Hadamard well-posedness for classes of non-Lipschitz semilinear parabolic partial differential equations

  • J. C. Meyer (a1) and D. J. Needham (a1)

Extract

We study classical solutions of the Cauchy problem for a class of non-Lipschitz semilinear parabolic partial differential equations in one spatial dimension with sufficiently smooth initial data. When the nonlinearity is Lipschitz continuous, results concerning existence, uniqueness and continuous dependence on initial data are well established (see, for example, the texts of Friedman and Smoller and, in the context of the present paper, see also Meyer), as are the associated results concerning Hadamard well-posedness. We consider the situations when the nonlinearity is Hölder continuous and when the nonlinearity is upper Lipschitz continuous. Finally, we consider the situation when the nonlinearity is both Hölder continuous and upper Lipschitz continuous. In each case we focus upon the question of existence, uniqueness and continuous dependence on initial data, and thus upon aspects of Hadamard well-posedness.

Copyright

Keywords

MSC classification

Aspects of Hadamard well-posedness for classes of non-Lipschitz semilinear parabolic partial differential equations

  • J. C. Meyer (a1) and D. J. Needham (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed