Global secondary bifurcation in a non-linear boundary value problem

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    Abstract

    We consider a steady-state non-linear boundary value problem which arises in modelling the formation of vascular networks in response to tumour growth. Global bifurcation from both trivial and non-trivial solution branches is considered, with emphasis on the latter. By investigating such secondary bifurcation, it is shown that positive, bounded solutions exist for all physically relevant values of a critical parameter. A certain class of these solutions is discussed with respect to the application to tumour growth.
    Original languageEnglish
    Pages (from-to)80-91
    Number of pages12
    JournalJournal of Mathematical Analysis and Applications
    Volume240
    Issue number1
    DOIs
    Publication statusPublished - 1 Dec 1999

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