Global stability of wavefronts with minimal speeds for nonlocal dispersal equations with degenerate

Abstract This paper is concerned with the global stability of wavefronts with minimal speeds for degenerate nonlocal dispersal equations. By the method of super- and subsolutions and a squeezing technique, the wavefront with minimal speed is proved to be globally asymptotically stable with phase shift.

[1]  Xiao-Qiang Zhao,et al.  Global asymptotic stability of minimal fronts in monostable lattice equations , 2008 .

[2]  Yi Li,et al.  Travelling Fronts in Cylinders and Their Stability , 1997 .

[3]  Wan-Tong Li,et al.  Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay , 2007 .

[4]  Klaus W. Schaaf Asymptotic behavior and traveling wave solutions for parabolic functional-differential equations , 1987 .

[5]  Paul C. Fife,et al.  Some Nonclassical Trends in Parabolic and Parabolic-like Evolutions , 2003 .

[6]  Emmanuel Chasseigne,et al.  Asymptotic behavior for nonlocal diffusion equations , 2006 .

[7]  Wan-Tong Li,et al.  Travelling wave fronts in nonlocal delayed reaction-diffusion systems and applications , 2009 .

[8]  Xiao-Qiang Zhao,et al.  Global Asymptotic Stability of Traveling Waves in Delayed Reaction-Diffusion Equations , 2000, SIAM J. Math. Anal..

[9]  Yaping Wu,et al.  Stability of traveling waves with critical speeds for $P$-degree Fisher-type equations , 2008 .

[10]  Jianhong Wu,et al.  Existence, Uniqueness and Asymptotic Stability of Traveling Wavefronts in A Non-Local Delayed Diffusion Equation , 2007 .

[11]  Yaping Wu,et al.  STABILITY OF TRAVELLING WAVES WITH ALGEBRAIC DECAY FOR n-DEGREE FISHER-TYPE EQUATIONS , 2006 .

[12]  Chi-Tien Lin,et al.  Traveling wavefronts for time-delayed reaction-diffusion equation: (II) Nonlocal nonlinearity , 2009 .

[13]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[14]  Wan-Tong Li,et al.  Travelling wave fronts in reaction-diffusion systems with spatio-temporal delays , 2006 .

[15]  Xinfu Chen,et al.  Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations , 1997, Advances in Differential Equations.

[16]  Yuan Lou,et al.  Random dispersal vs. non-local dispersal , 2009 .

[17]  Peter W. Bates,et al.  Spectral analysis and multidimensional stability of traveling waves for nonlocal Allen-Cahn equation , 2002 .

[18]  Wan-Tong Li,et al.  Entire solutions in the Fisher-KPP equation with nonlocal dispersal , 2010 .

[19]  P. Bates,et al.  Traveling Waves in a Convolution Model for Phase Transitions , 1997 .

[20]  Wan-Tong Li,et al.  Asymptotic behavior for nonlocal dispersal equations , 2010 .

[21]  Shuxia Pan,et al.  Existence and stability of traveling wavefronts in a nonlocal diffusion equation with delay , 2010 .

[22]  Yi Li,et al.  Local stability of traveling-wave solutions of nonlinear reaction-diffusion equations , 2006 .

[23]  Shiwang Ma,et al.  Asymptotic stability of traveling waves in a discrete convolution model for phase transitions , 2005 .

[24]  Ming Mei,et al.  On travelling wavefronts of Nicholson's blowflies equation with diffusion , 2010, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[25]  Jerome Coville,et al.  Nonlocal anisotropic dispersal with monostable nonlinearity , 2008, 1106.4531.

[26]  Xinfu Chen,et al.  Existence and Asymptotic Stability of Traveling Waves of Discrete Quasilinear Monostable Equations , 2002 .

[27]  Wan-Tong Li,et al.  Traveling Fronts in Monostable Equations with Nonlocal Delayed Effects , 2008 .

[28]  Jérôme Coville,et al.  On a non-local equation arising in population dynamics , 2007, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[29]  J. Medlock,et al.  Spreading disease: integro-differential equations old and new. , 2003, Mathematical biosciences.

[30]  Structural stability of travelling waves in an integrodifferential equation , 2008 .