An inhomogeneous nonlocal diffusion problem with unbounded steps
| Autor: | Salomé Martínez, Manuel Elgueta, Jorge García-Melián, Carmen Cortázar |
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| Rok vydání: | 2015 |
| Předmět: |
Pure mathematics
Diffusion problem Kernel (set theory) media_common.quotation_subject 010102 general mathematics Mathematical analysis Hölder condition Infinity Positive function 01 natural sciences 010101 applied mathematics Nonlinear system Mathematics (miscellaneous) Uniqueness 0101 mathematics Unit (ring theory) media_common Mathematics |
| Zdroj: | Journal of Evolution Equations. 16:209-232 |
| ISSN: | 1424-3202 1424-3199 |
| DOI: | 10.1007/s00028-015-0299-x |
| Popis: | We consider the following nonlocal equation $$\int J\left(\frac{x-y}{g(y)} \right) \frac{u(y)}{g(y)} dy -u(x)=0\qquad x\in \mathbb{R},$$ where J is an even, compactly supported, Holder continuous kernel with unit integral and g is a continuous positive function. Our main concern will be with unbounded functions g, contrary to previous works. More precisely, we study the influence of the growth of g at infinity on the integrability of positive solutions of this equation, therefore determining the asymptotic behavior as \({t\to +\infty}\) of the solutions to the associated evolution problem in terms of the growth of g. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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