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Temporal decay of solutions for a chemotaxis model of angiogenesis type

김명현|안재욱
대한수학회 (The Korean Mathematical Society)|2023.05|대한수학회지 (Journal of the KMS)|제60권 제3호|pp. 619-634|DOI 10.4134/JKMS.j220424

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키워드

angiogenesisAnderson-Chaplain modeltemporal decay
주제분류수학

초록

This paper considers a parabolic-hyperbolic-hyperbolic type chemotaxis system in $\R^{d}$, $d\ge3$, describing tumor-induced angiogenesis. The global existence result and temporal decay estimate for a unique mild solution are established under the assumption that some Sobolev norms of initial data are sufficiently small.

Abstract

This paper considers a parabolic-hyperbolic-hyperbolic type chemotaxis system in $\R^{d}$, $d\ge3$, describing tumor-induced angiogenesis. The global existence result and temporal decay estimate for a unique mild solution are established under the assumption that some Sobolev norms of initial data are sufficiently small.

참고문헌 (15)

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  10. P. Monaghan, "Topographical arrangement of basement membrane proteins in lactating rat mammary gland: Comparison of the distribution of type IV collagen, laminin, fibronectin and Thy-1 at the ultrastructural level", Proc. Nat. Acad. Sci, 80, pp.3344~3348 (1983)
  11. V. R. Muthukkaruppan, "Tumor-induced neovascularization in the mouse eye", J. Natl. Cancer Inst, 69, pp.699~705 (1982)
  12. B. Perthame, "Regularization in Keller-Segel type systems and the De Giorgi method", Commun. Math. Sci, 10(2), pp.463~476 (2012)[DOI]
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  14. Y. Sugiyama, "Global solutions to a chemotaxis system with non-diffusive memory", J. Math. Anal. Appl, 410(2), pp.908~917 (2014)[DOI]
  15. T. Suzuki, "Global in time solution to a class of tumor growth systems", Adv. Math. Sci. Appl, 19(2), pp.503~524 (2009)

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