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This paper considers a parabolic-hyperbolic-hyperbolic type chemotaxis system in ℝ𝑑, 𝑑≥3, 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.

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참고문헌 (15건) : 자료제공( 네이버학술정보 )

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번호 참고문헌 국회도서관 소장유무
1 A. R. A. Anderson and M. A. J. Chaplain, Continuous and discrete mathematical models of tumor-induced angiogenesis, Bull. Math. Bio. 60 (1998), 857–899. 미소장
2 J. C. Bowersox and N. Sorgente, Chemotaxis of aortic endothelial cells in response to fibronectin, Cancer Res. 42 (1982), 2547–2551. 미소장
3 M. Chae, K. Kang, and J. Lee, Global existence and temporal decay in Keller-Segel models coupled to fluid equations, Comm. Partial Differential Equations 39 (2014), no. 7, 1205–1235. https://doi.org/10.1080/03605302.2013.852224 미소장
4 L. Corrias, B. Perthame, and H. Zaag, A chemotaxis model motivated by angiogenesis, C. R. Math. Acad. Sci. Paris 336 (2003), no. 2, 141–146. https://doi.org/10.1016/S1631-073X(02)00008-0 미소장
5 L. Corrias, B. Perthame, and H. Zaag, Global solutions of some chemotaxis and angiogenesis systems in high space dimensions, Milan J. Math. 72 (2004), 1–28. https://doi.org/10.1007/s00032-003-0026-x 미소장
6 J. Folkman and M. Klasgsburn, Angiogenic factors, Science 235 (1987), 442–447. 미소장
7 A. Friedman and J. Tello, Stability of solutions of chemotaxis equations in reinforced random walks, J. Math. Anal. Appl. 272 (2002), no. 1, 138–163. https://doi.org/10.1016/S0022-247X(02)00147-6 미소장
8 A. Kubo and T. Suzuki, Mathematical models of tumour angiogenesis, J. Comput. Appl. Math. 204 (2007), no. 1, 48–55. https://doi.org/10.1016/j.cam.2006.04.027 미소장
9 L. A. Liotta, C. N. Rao, and S. H. Barsky, Tumor invasion and the extracellular matrix, Lab. Invest. 49 (1983), 636–649. 미소장
10 P. Monaghan, M. J. Warburton, N. Perusinghe, and P. S. Rutland, 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 (1983), 3344–3348. 미소장
11 V. R. Muthukkaruppan, L. Kubai, and R. Auerbach, Tumor-induced neovascularization in the mouse eye, J. Natl. Cancer Inst. 69 (1982), 699–705. 미소장
12 B. Perthame and A. F. Vasseur, Regularization in Keller-Segel type systems and the De Giorgi method, Commun. Math. Sci. 10 (2012), no. 2, 463–476. https://doi.org/10. 4310/CMS.2012.v10.n2.a2 미소장
13 S. L. Schor, A. M. Schor, and G. W. Brazill, The effects of fibronectin on the migration of human foreskin fibroblasts and Syrian hamster melanoma cells into three-dimensional gels of native collagen fibres, J. Cell Sci. 48 (1981), 301–314. 미소장
14 Y. Sugiyama, Y. Tsutsui, and J. J. L. Vel´azquez, Global solutions to a chemotaxis system with non-diffusive memory, J. Math. Anal. Appl. 410 (2014), no. 2, 908–917. https://doi.org/10.1016/j.jmaa.2013.08.065 미소장
15 T. Suzuki and R. Takahashi, Global in time solution to a class of tumor growth systems, Adv. Math. Sci. Appl. 19 (2009), no. 2, 503–524. 미소장

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