Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations

By Jong-Shenq Guo, Y. Morita. 2004

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Existence and nonexistence of traveling waves for a nonlocal monostable equation (2008, background): “, [5, 7, 10, 11, 12, 13, 14, 15, 18, 19, 23, 24, 26, 27, 28] on traveling waves and long-time behavior in various monostable evolution systems, [2, 4, 30] nonlocal bistable equations and [20] Euler equation.”
Entire solutions in monostable reaction-diffusion equations with delayed nonlinearity (2008, background): “In particular, Chen and Guo [6], Chen et al. [7], Fukao et al. [10], Guo and Morita [13], Hamel and Nadirashvili [14,15] and Morita and Ninomiya [20] have shown that the study of entire solutions is essential for a full understanding of the transient dynamics and the structures of the global attract”
Entire solutions in reaction-advection-diffusion equations in cylinders (2008, unknown): “We should also mention that Morita and Ninomiya [25] obtained some novel entire solutions which are completely different from these observed in [10,11,16,18,19,37].”
Bistable traveling waves around an obstacle (2009, methodology): “For the supersolution, we rely in part on a technique of Guo and Morita [11], in which they used a similar supersolution to study an entire solution having a pair of mutually annihilating fronts.”
Existence and uniqueness of entire solutions for a reaction-diffusion equation (2005, methodology): “In [16], sub- and super-solutions are constructed by different methods.”