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Abstract:

In this paper we prove decay estimates for solutions to a nonlocal p-Laplacian evolution problem with mixed boundary conditions, that is, (Formula presented.) for (x, t) ∈ Ω × ℝ+ and u(x, t) = 0 in Ω0 × ℝ+. The proof of these estimates is based on bounds for the associated first eigenvalue.

Registro:

Documento: Artículo
Título:Decay estimates for a nonlocal p-Laplacian evolution problem with mixed boundary conditions
Autor:Ferreira, R.; Rossi, J.D.
Filiación:Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Madrid, 28040, Spain
Departamento de Análisis Matemático, Universidad de Alicante, Ap. correos 99, Alicante, 03080, Spain
Dpto. de Matemáticas, FCEyN, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
Palabras clave:Eigenvalues; Nonlocal diffusion
Año:2015
Volumen:35
Número:4
Página de inicio:1469
Página de fin:1478
DOI: http://dx.doi.org/10.3934/dcds.2015.35.1469
Título revista:Discrete and Continuous Dynamical Systems- Series A
Título revista abreviado:Discrete Contin. Dyn. Syst. Ser A
ISSN:10780947
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10780947_v35_n4_p1469_Ferreira

Referencias:

  • Andreu, F., Mazon, J.M., Rossi, J.D., Toledo, J., The Neumann problem for nonlocal nonlinear diffusion equations (2008) J. Evol. Eqns., 8, pp. 189-215
  • Andreu, F., Mazon, J.M., Rossi, J.D., Toledo, J., A nonlocal p-Laplacian evolution equation with Neumann boundary conditions (2008) J. Math. Pures Appl., 90, pp. 201-227
  • Andreu, F., Mazón, J.M., Rossi, J.D., Toledo, J., (2010) Nonlocal Diffusion Problems, 165. , Amer. Math. Soc. Mathematical Surveys and Monographs
  • Bates, P., Chen, X., Chmaj, A., Heteroclinic solutions of a van der Waals model with indefinite nonlocal interactions (2005) Calc. Var., 24, pp. 261-281
  • Bates, P., Fife, P., Ren, X., Wang, X., Traveling waves in a convolution model for phase transitions (1997) Arch. Rat. Mech. Anal., 138, pp. 105-136
  • Chasseigne, E., Chaves, M., Rossi, J.D., Asymptotic behavior for nonlocal diffusion equations (2006) J. Math. Pures Appl., 86, pp. 271-291
  • Cortázar, C., Elgueta, M., Rossi, J.D., Wolanski, N., Boundary fluxes for nonlocal diffusion (2007) J. Diff. Eqns., 234, pp. 360-390
  • Cortázar, C., Elgueta, M., Rossi, J.D., Wolanski, N., How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems (2008) Arch. Rat. Mech. Anal., 187, pp. 137-156
  • Coville, J., Dupaigne, L., On a nonlocal equation arising in population dynamics (2007) Proc. Roy. Soc. Edinburgh, 137, pp. 727-755
  • Du, Q., Gunzburger, M., Lehoucq, R., Zhou, K., A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws (2013) Math. Mod. Meth. Appl. Sci., 23, pp. 493-540
  • Fife, P., Some nonclassical trends in parabolic and parabolic-like evolutions (2003) Trends in Nonlinear Analysis, pp. 153-191. , Springer-Verlag, Berlin
  • García-Melián, J., Rossi, J.D., On the principal eigenvalue of some nonlocal diffusion problems (2009) J. Differential Equations, 246, pp. 21-38
  • Hutson, V., Martínez, S., Mischaikow, K., Vickers, G.T., The evolution of dispersal (2003) J. Math. Biol., 47, pp. 483-517
  • Ignat, L.I., Rossi, J.D., Decay estimates for nonlocal problems via energy methods (2009) J. Math. Pures Appl., 92, pp. 163-187
  • Krein, M.G., Rutman, M.A., Linear operators leaving invariant a cone in a Banach space (1950) Amer. Math. Soc. Transl., 1950, pp. 199-325
  • Parks, M.L., Lehoucq, R.B., Plimpton, S., Silling, S., Implementing peridynamics within a molecular dynamics code (2008) Computer Physics Comm., 179, pp. 777-783
  • Silling, S.A., Reformulation of elasticity theory for discontinuities and long-range forces (2000) J. Mech. Phys. Solids, 48, pp. 175-209
  • Silling, S.A., Lehoucq, R.B., Convergence of peridynamics to classical elasticity theory (2008) J. Elasticity, 93, pp. 13-37

Citas:

---------- APA ----------
Ferreira, R. & Rossi, J.D. (2015) . Decay estimates for a nonlocal p-Laplacian evolution problem with mixed boundary conditions. Discrete and Continuous Dynamical Systems- Series A, 35(4), 1469-1478.
http://dx.doi.org/10.3934/dcds.2015.35.1469
---------- CHICAGO ----------
Ferreira, R., Rossi, J.D. "Decay estimates for a nonlocal p-Laplacian evolution problem with mixed boundary conditions" . Discrete and Continuous Dynamical Systems- Series A 35, no. 4 (2015) : 1469-1478.
http://dx.doi.org/10.3934/dcds.2015.35.1469
---------- MLA ----------
Ferreira, R., Rossi, J.D. "Decay estimates for a nonlocal p-Laplacian evolution problem with mixed boundary conditions" . Discrete and Continuous Dynamical Systems- Series A, vol. 35, no. 4, 2015, pp. 1469-1478.
http://dx.doi.org/10.3934/dcds.2015.35.1469
---------- VANCOUVER ----------
Ferreira, R., Rossi, J.D. Decay estimates for a nonlocal p-Laplacian evolution problem with mixed boundary conditions. Discrete Contin. Dyn. Syst. Ser A. 2015;35(4):1469-1478.
http://dx.doi.org/10.3934/dcds.2015.35.1469