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Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on Mathbb{R}
The author considers semilinear parabolic equations of the form u_t=u_xx+f(u),\quad x\in \mathbb R,t>0, where f a C^1 function. Assuming that 0 and \gamma >0 are constant steady states, the author investigates the large-time behavior of the front-like solutions, that is, solutions u whose init...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2020.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1278. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | The author considers semilinear parabolic equations of the form u_t=u_xx+f(u),\quad x\in \mathbb R,t>0, where f a C^1 function. Assuming that 0 and \gamma >0 are constant steady states, the author investigates the large-time behavior of the front-like solutions, that is, solutions u whose initial values u(x,0) are near \gamma for x\approx -\infty and near 0 for x\approx \infty . If the steady states 0 and \gamma are both stable, the main theorem shows that at large times, the graph of u(\cdot ,t) is arbitrarily close to a propagating terrace (a system of stacked traveling fonts). The author. |
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| Descripción Física: | 1 online resource (100 p.). |
| Bibliografía: | Includes bibliographical references. |
| ISBN: | 9781470458065 1470458063 |