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Abstract:

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.

Registro:

Documento: Artículo
Título:Decay estimates for nonlinear nonlocal diffusion problems in the whole space
Autor:Ignat, L.I.; Pinasco, D.; Rossi, J.D.; San Antolin, A.
Filiación:Institute of Mathematics Simion Stoilow of the Romanian Academy, 21 Calea Grivitei Street, 010702 Bucharest, Romania
University of Bucharest, 14 Academiei Str., 010014 Bucharest, Romania
Departamento de Matemáticas y Estadística, Universidad Torcuato di Tella, Miñones 2177, C1428ATG Ciudad Autónoma de Buenos Aires, Argentina
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Ciudad Autónoma de Buenos Aires, Buenos Aires, Argentina
Departamento de Análisis Matemático, Universidad de Alicante, Ap. Correos 99, 03080 Alicante, Spain
Dpto. De Matemáticas, FCEyN, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Año:2014
Volumen:122
Número:1
Página de inicio:375
Página de fin:401
DOI: http://dx.doi.org/10.1007/s11854-014-0011-z
Título revista:Journal d'Analyse Mathematique
Título revista abreviado:J. Anal. Math.
ISSN:00217670
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00217670_v122_n1_p375_Ignat

Referencias:

  • Andreu, F., Mazon, J.M., Rossi, J.D., Toledo, J., The Neumann problem for nonlocal nonlinear diffusion equations (2008) J. Evol. Equ., 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. (9), 90, pp. 201-227
  • Andreu, F., Mazón, J.M., Rossi, J.D., Toledo, J., The limit as p → ∞ in a nonlocal p-Laplacian evolution equation. A nonlocal approximation of a model for sandpiles (2009) Calc. Var. Partial Differential Equations, 35, pp. 279-316
  • Andreu, F., Mazón, J.M., Rossi, J.D., Toledo, J., A nonlocal p-Laplacian evolution equation with nonhomogeneous Dirichlet boundary conditions (2009) SIAM J. Math. Anal., 40, pp. 1815-1851
  • Andreu, F., Mazón, J.M., Rossi, J.D., Toledo, J., (2010) Nonlocal Diffusion Problems, , Providence RI: Amer. Math. Soc
  • Bachman, G., Narici, L., (2000) Functional Analysis, , New York: Dover
  • Bates, P., Chen, X., Chmaj, A., Heteroclinic solutions of a van der Waals model with indefinite nonlocal interactions (2005) Calc. Var. Partial Differential Equations, 24, pp. 261-281
  • Bates, P., Fife, P., Ren, X., Wang, X., Traveling waves in a convolution model for phase transitions (1997) Arch. Rational 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
  • Chmaj, A., Ren, X., Homoclinic solutions of an integral equation: existence and stability (1999) J. Differential Equations, 155, pp. 17-43
  • Cortázar, C., Coville, J., Elgueta, M., Martínez, S., A non local inhomogeneous dispersal process (2007) J. Differential Equations, 241, pp. 332-358
  • Cortázar, C., Elgueta, M., Rossi, J.D., A nonlocal diffusion equation whose solutions develop a free boundary (2005) Ann. Henri Poincaré, 6, pp. 269-281
  • Cortázar, C., Elgueta, M., Rossi, J.D., Wolanski, N., Boundary fluxes for nonlocal diffusion (2007) J. Differential Equations, 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. Rational Mech. Anal., 187, pp. 137-156
  • Coville, J., On uniqueness and monotonicity of solutions on non-local reaction diffusion equations (2006) Ann. Mat. Pura Appl. (4), 185, pp. 461-485
  • Coville, J., On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators (2010) J. Differential Equations, 249, pp. 2921-2953
  • Coville, J., Dupaigne, L., On a nonlocal equation arising in population dynamics (2007) Proc. Roy. Soc. Edinburgh Sec. A, 137, pp. 1-29
  • Du, Q., Gunzburger, M., Lehoucq, R., Zhou, K., A nonlocal vector calculus, non-local volume-constrained problems, and nonlocal balance laws (2013) Math. Models Methods 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. , Berlin: Springer-Verlag
  • García-Melián, J., Rossi, J.D., Maximum and antimaximum principles for some nonlocal diffusion operators (2009) Nonlinear Anal., 71, pp. 6116-6121
  • García-Melián, J., Rossi, J.D., On the principal eigenvalue of some nonlocal diffusion problems (2009) J. Differential Equations, 246, pp. 21-38
  • Gilbarg, D., Trudinger, N., (2001) Elliptic Partial Differential Equations of Second Order, , Berlin: Springer-Verlag
  • 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., A nonlocal convection-diffusion equation (2007) J. Funct. Anal., 251, pp. 399-437
  • Ignat, L.I., Rossi, J.D., Decay estimates for nonlocal problems via energy methods (2009) J. Math. Pures Appl. (9), 92, pp. 163-187
  • Ignat, L.I., Rossi, J.D., San Antolin, A., Lower and upper bounds for the first eigenvalue of nonlocal diffusion problems in the whole space (2012) J. Differential Equations, 252, pp. 6429-6447
  • Krein, M.G., Rutman, M.A., Linear operators leaving invariant a cone in a Banach space (1962) Amer. Math. Soc. Transl., 10, pp. 199-325
  • Parks, M.L., Lehoucq, R.B., Plimpton, S., Silling, S., Implementing peridynamics within a molecular dynamics code (2008) Comput. Physics Comm., 179, pp. 777-783
  • Shen, W., Zhang, A., Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats (2010) J. Differential Equations, 249, pp. 747-795
  • 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 ----------
Ignat, L.I., Pinasco, D., Rossi, J.D. & San Antolin, A. (2014) . Decay estimates for nonlinear nonlocal diffusion problems in the whole space. Journal d'Analyse Mathematique, 122(1), 375-401.
http://dx.doi.org/10.1007/s11854-014-0011-z
---------- CHICAGO ----------
Ignat, L.I., Pinasco, D., Rossi, J.D., San Antolin, A. "Decay estimates for nonlinear nonlocal diffusion problems in the whole space" . Journal d'Analyse Mathematique 122, no. 1 (2014) : 375-401.
http://dx.doi.org/10.1007/s11854-014-0011-z
---------- MLA ----------
Ignat, L.I., Pinasco, D., Rossi, J.D., San Antolin, A. "Decay estimates for nonlinear nonlocal diffusion problems in the whole space" . Journal d'Analyse Mathematique, vol. 122, no. 1, 2014, pp. 375-401.
http://dx.doi.org/10.1007/s11854-014-0011-z
---------- VANCOUVER ----------
Ignat, L.I., Pinasco, D., Rossi, J.D., San Antolin, A. Decay estimates for nonlinear nonlocal diffusion problems in the whole space. J. Anal. Math. 2014;122(1):375-401.
http://dx.doi.org/10.1007/s11854-014-0011-z