Abstract
We consider the following nonlocal equation
where J is an even, compactly supported, Hölder 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.
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Cortázar, C., Elgueta, M., García-Melián, J. et al. An inhomogeneous nonlocal diffusion problem with unbounded steps. J. Evol. Equ. 16, 209–232 (2016). https://doi.org/10.1007/s00028-015-0299-x
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DOI: https://doi.org/10.1007/s00028-015-0299-x