A priori bounds and global existence of solutions of the steady-state Sel'kov model

F. A. Davidson (Lead / Corresponding author), B. P. Rynne (Lead / Corresponding author)

    Research output: Contribution to journalArticle

    38 Citations (Scopus)

    Abstract

    We consider the system of reaction-diffusion equations known as the Sel'kov model. This model has been applied to various problems in chemistry and biology. We obtain a priori bounds on the size of the positive steady-state solutions of the system defined on bounded domains in Rn, 1 ≤ n ≤ 3 (this is the physically relevant case). Previously, such bounds had been obtained in the case n = 1 under more restrictive hypotheses. We also obtain regularity results on the smoothness of such solutions and show that non-trivial solutions exist for a wide range of parameter values.
    Original languageEnglish
    Pages (from-to)507-516
    Number of pages10
    JournalProceedings of the Royal Society of Edinburgh, Section A : Mathematics
    Volume130
    Issue number3
    DOIs
    Publication statusPublished - Jun 2000

    Cite this

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    title = "A priori bounds and global existence of solutions of the steady-state Sel'kov model",
    abstract = "We consider the system of reaction-diffusion equations known as the Sel'kov model. This model has been applied to various problems in chemistry and biology. We obtain a priori bounds on the size of the positive steady-state solutions of the system defined on bounded domains in Rn, 1 ≤ n ≤ 3 (this is the physically relevant case). Previously, such bounds had been obtained in the case n = 1 under more restrictive hypotheses. We also obtain regularity results on the smoothness of such solutions and show that non-trivial solutions exist for a wide range of parameter values.",
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    A priori bounds and global existence of solutions of the steady-state Sel'kov model. / Davidson, F. A. (Lead / Corresponding author); Rynne, B. P. (Lead / Corresponding author).

    In: Proceedings of the Royal Society of Edinburgh, Section A : Mathematics, Vol. 130, No. 3, 06.2000, p. 507-516.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - A priori bounds and global existence of solutions of the steady-state Sel'kov model

    AU - Davidson, F. A.

    AU - Rynne, B. P.

    PY - 2000/6

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    N2 - We consider the system of reaction-diffusion equations known as the Sel'kov model. This model has been applied to various problems in chemistry and biology. We obtain a priori bounds on the size of the positive steady-state solutions of the system defined on bounded domains in Rn, 1 ≤ n ≤ 3 (this is the physically relevant case). Previously, such bounds had been obtained in the case n = 1 under more restrictive hypotheses. We also obtain regularity results on the smoothness of such solutions and show that non-trivial solutions exist for a wide range of parameter values.

    AB - We consider the system of reaction-diffusion equations known as the Sel'kov model. This model has been applied to various problems in chemistry and biology. We obtain a priori bounds on the size of the positive steady-state solutions of the system defined on bounded domains in Rn, 1 ≤ n ≤ 3 (this is the physically relevant case). Previously, such bounds had been obtained in the case n = 1 under more restrictive hypotheses. We also obtain regularity results on the smoothness of such solutions and show that non-trivial solutions exist for a wide range of parameter values.

    U2 - 10.1017/S0308210500000275

    DO - 10.1017/S0308210500000275

    M3 - Article

    VL - 130

    SP - 507

    EP - 516

    JO - Proceedings of the Royal Society of Edinburgh, Section A : Mathematics

    JF - Proceedings of the Royal Society of Edinburgh, Section A : Mathematics

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