| Автор | Doole, S. H. |
| Дата выпуска | 1994 |
| dc.description | A class of initial-boundary value problems with a conserved first integral is studied. The class of problems includes particular cases of interest. In one parameter limit, the equations arise as a similarity reduction of the Navier-Stokes equations, which has been recently studied for its blow-up properties, and in another, a class of scalar reaction-diffusion equations, modified by the addition of a non-local non-linearity to ensure conservation of the first integral. Once the problem has been stated, it is shown how it may be derived from the Navier-Stokes equations in one parameter limit. Steady-state solutions are then constructed using a rigorous iterative method which we call Crandall Iteration. The steady solution set includes, in a particular parameter limit, those of the Cahn-Hilliard equation. Amplitude expansions and centre manifold theory are employed to analyze the heteroclinic orbits connecting these steady solutions. It is proved that Hopf bifurcation of periodic solutions cannot occur |
| Формат | application.pdf |
| Издатель | Journals Oxford Ltd |
| Копирайт | Copyright Taylor and Francis Group, LLC |
| Название | Dynamic bifurcation in a system of PDES with a conserved first integral |
| Тип | research-article |
| DOI | 10.1080/02681119408806178 |
| Electronic ISSN | 1465-3389 |
| Print ISSN | 0268-1110 |
| Журнал | Dynamics and Stability of Systems |
| Том | 9 |
| Первая страница | 197 |
| Последняя страница | 213 |
| Аффилиация | Doole, S. H.; Department of Engineering Mathematics, University of Bristol |
| Выпуск | 3 |
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