Decay estimates for nonlinear nonlocal diffusion problems in the whole space

@article{Ignat2012DecayEF,
  title={Decay estimates for nonlinear nonlocal diffusion problems in the whole space},
  author={L. Ignat and Dami{\'a}n Pinasco and J. Rossi and A. S. Antol{\'i}n},
  journal={Journal d'Analyse Math{\'e}matique},
  year={2012},
  volume={122},
  pages={375-401}
}
AbstractIn this paper, we obtain bounds for the decay rate in the Lr (ℝd)-norm for the solutions of a nonlocal and nonlinear evolution equation, namely, $$u_t \left( {x,t} \right) = \int_{\mathbb{R}^d } {K\left( {x,y} \right)\left| {u\left( {y,t} \right) - u\left( {x,t} \right)} \right|^{p - 2} \left( {u\left( {y,t} \right) - u\left( {x,t} \right)} \right)dy, x \in \mathbb{R}^d , t > 0.}$$. We consider a kernel of the form K(x, y) = ψ(y−a(x)) + ψ(x−a(y)), where ψ is a bounded, nonnegative… Expand
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