Fractional decay bounds for nonlocal zero order heat equations
| Autor: | Chasseigne, Emmanuel, Felmer, Patricio, Rossi, J., Topp, Erwin |
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| Rok vydání: | 2013 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper we obtain bounds for the decay rate for solutions to the nonlocal problem $\partial_t u(t,x) = \int_{\R^n} J(x,y)[u(t,y) - u(t,x)] dy$. Here we deal with bounded kernels $J$ but with polynomial tails, that is, we assume a lower bound of the form $J(x,y) \geq c_1|x-y|^{-(n + 2\sigma)}$, for $|x - y| > c_2$. Our estimates takes the form $\|u(t)\|_{L^q(\R^n)} \leq C t^{-\frac{n}{2\sigma} (1 - \frac{1}{q})}$ for $t$ large. |
| Databáze: | arXiv |
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