Decay estimates for nonlinear nonlocal diffusion problems in the whole space
In 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, (Formula presented.). We consider a kernel of the form K(x, y) = ψ(y-a(x)) + ψ(x-a(y)), where ψ is a bounded, nonnegative function supported in the unit ba...
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| Autores principales: | , , , |
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| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00217670_v122_n1_p375_Ignat |
| Aporte de: |
| Sumario: | In 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, (Formula presented.). We consider a kernel of the form K(x, y) = ψ(y-a(x)) + ψ(x-a(y)), where ψ is a bounded, nonnegative function supported in the unit ball and a is a linear function a(x) = Ax. To obtain the decay rates, we derive lower and upper bounds for the first eigenvalue of a nonlocal diffusion operator of the form (Formula presented.). The upper and lower bounds that we obtain are sharp and provide an explicit expression for the first eigenvalue in the whole space ℝd: (Formula presented.) Moreover, we deal with the p = ∞ eigenvalue problem, studying the limit of λ1,p 1/p as p→∞. © 2014 Hebrew University Magnes Press. |
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