Generalized fronts in reaction-diffusion equations with mono-stable nonlinearity |
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Authors: | Yaqin Shu Wan-Tong LiNai-Wei Liu |
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Institution: | a School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of Chinab School of Mathematics and Informational Science, Yantai University, Yantai, Shandong 264005, People’s Republic of China |
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Abstract: | We consider transition fronts (generalized traveling fronts) of mono-stable reaction-diffusion equations with spatially inhomogeneous nonlinearity. By constructing a cutoff function and using an approximate method, we establish the existence of transition fronts of the equation. Furthermore, we give the uniform non-degeneracy estimates of the solutions, such as a lower bound on the time derivative on some level sets, as well as an upper bound on the spatial derivative. |
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Keywords: | 35K57 35B40 34K30 58D25 |
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