Traveling wave front and stability as planar wave of reaction diffusion equations with nonlocal delays

Zeitschrift für angewandte Mathematik und Physik - Tập 64 Số 4 - Trang 1005-1023 - 2013
Guangying Lv1, Mingxin Wang2
1Institute of Contemporary Mathematics, Henan University, Kaifeng, People’s Republic of China
2Natural Science Research Center, Harbin Institute of Technology, Harbin, People’s Republic of China

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Tài liệu tham khảo

Ai S.: Traveling wavefronts for generalized Fisher equation with spatio-temporal delays. J. Differ. Equ. 232, 104–133 (2007)

Allen S., Cahn J.W.: A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta. Metall. 27, 1084–1095 (1979)

Ashwin P., Bartuccelli M.V., Gourley S.A.: Traveling fronts for the KPP equation with spatio-temporal delay. Z. Angew. Math. Phys. 53, 103–122 (2002)

Conley C., Gardner R.: An application of the generalized Morse index to travelling wave solutions of a competitive reaction diffusion model. Indiana Univ. Math. J. 33, 319–343 (1984)

Fenichel N.: Geometric singular perturbation theory for ordinary differential equations. J. Differ. Equ. 31, 53–98 (1979)

Gourley S.A., Ruan S.G.: Convergence and traveling fronts in functional differential equations with nonlocal terms: a competition model. SIAM. J. Math. Anal. 35, 806–822 (2003)

Huang W.Z.: Uniqueness of bistable traveling wave for mutualist species. J. Dyn. Differ. Equ. 13, 147–183 (2001)

Jones, C.K.R.T.: Geometric Singular Perturbation Theory. Lecture Notes in Mathematics, Vol. 1609. Springer, Berlin (1995)

Kapitula T.: Mutlidimensional stability of planar traveling waves. Trans. Am. Math. Soc. 349, 257–269 (1997)

Levermore C.D., Xin J.X.: Multidimensional stability of traveling waves in a bistable reaction diffusion equation II. Commun. Partial Differ. Equ. 17, 1901–1924 (1992)

Li W.T., Wang Z.C.: Traveling fronts in diffusive and cooperative Lotka–Volterra system with nonlocal delays. Z. Angew. Math. Phys. 58, 571–591 (2007)

Lin G., Li W.T.: Bistable wavefronts in a diffusive and competitive Lotka–Volterra type system with delays. J. Differ. Equ. 244, 487–513 (2008)

Lv G.Y., Wang M.X.: Existence, uniqueness and asymptotic behavior of traveling wave fronts of a vector disease model. Nonlinear Anal. RWA 11, 2035–2043 (2010)

Lv G.Y., Wang M.X.: Stability of planar waves in mono-stable reaction diffusion equation. Proc. Am. Math. Soc. 139, 3611–3621 (2011)

Lv G.Y., Wang M.X.: Stability of planar waves in reaction-diffusion system. Sci. China Ser. A Math 54, 1403–1419 (2011)

Matano H., Nara M., Taniguchi M.: Stability of planar waves in the Allen-Cahn equation. Commun. Partial Differ. Equ. 34, 976–1002 (2009)

Mischaikow K., Hutson V.: Traveling waves for mutualist species. SIAM. J. Math. Anal. 24, 987–1008 (1993)

Ou C., Wu J.: Persistence of wavefronts in delayed non-local reaction diffusion equations. J. Differ. Equ. 235, 219–261 (2007)

Volpert A.I., Volpert V.A., Volpert V.A.: Traveling Wave Solutions of Parabolic Systems. Translation of Mathematical Monographs, Vol. 140. American Mathematical Society, Providence (1994)

Wang Z.C., Li W.T., Ruan S.G.: Traveling wave fronts in reaction diffusion systems with spatio-temporal delays. J. Differ. Equ. 222, 185–232 (2006)

Wang Z.C., Li W.T., Ruan S.G.: Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay. J. Differ. Equ. 238, 153–200 (2007)

Xin J.X.: Multidimensional stability of traveling waves in a bistable reaction diffusion equation I. Commun. Partial Differ. Equ. 17, 1889–1899 (1992)