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math.AP2012
Decay estimates for nonlinear nonlocal diffusion problems in the whole space
Liviu I. Ignat, Damián Pinasco, Julio D. Rossi +1
In this paper we obtain bounds for the decay rate in the $L^r (\rr^d)$-norm for the solutions to a nonlocal and nolinear evolution equation, namely, $$u_t(x,t) = \int_{\rr^d} K(x,y…
math.AP2011
Lower and upper bounds for the first eigenvalue of nonlocal diffusion problems in the whole space
L. I. Ignat, J. D. Rossi, A. San Antolin
We find lower and upper bounds for the first eigenvalue of a nonlocal diffusion operator of the form $ T(u) = - \int_{\rr^d} K(x,y) (u(y)-u(x)) \, dy$. Here we consider a kernel $K…