Navegar

Colección

Datos Estadísticas

Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We study evolution equations governed by an averaging operator on a directed tree, showing existence and uniqueness of solutions. In addition we find conditions of the initial condition that allows us to find the asymptotic decay rate of the solutions as t → ∞. It turns out that this decay rate is not uniform, it strongly depends on how the initial condition goes to zero as one goes down in the tree. © European Mathematical Society.

Registro:

Documento: Artículo
Título:Existence, uniqueness and decay rates for evolution equations on trees
Autor:Del Pezzo, L.M.; Mosquera, C.A.; Rossi, J.D.
Filiación:Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellon I, Ciudad Universitaria (1428), Buenos Aires, Argentina
Departamento de Aná lisis Matemático, Universidad de Alicante, Ap. correo 99, 03080, Alicante, Spain
Palabras clave:Averaging operators; Decay estimates; Evolution equations
Año:2014
Volumen:71
Número:1
Página de inicio:63
Página de fin:77
DOI: http://dx.doi.org/10.4171/PM/1941
Título revista:Portugaliae Mathematica
Título revista abreviado:Port. Math.
ISSN:00325155
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00325155_v71_n1_p63_DelPezzo

Referencias:

  • Alvarez, V., Rodríguez, J.M., Yakubovich, D.V., Estimates for nonlinear harmonic "measures"on trees (2001) Michigan Math. J, 49, pp. 47-64. , Zbl 1006.31006 MR 1827075
  • Del Pezzo, L.M., Mosquera, C.A., Rossi, J.D., The unique continuation property for a nonlinear equation on trees J. London Math. Soc., , To appear doi: 10.1112/jlms/jdt067
  • Chung, S.-Y., Berenstein, C.A., O-harmonic functions and inverse conductivity problems on networks (2005) SIAM J. Appl. Math., 65, pp. 1200-1226. , Zbl 1068.05040 MR 2147325
  • Curtis, E.B., Morrow, J.A., Determining the resistors in a network (1990) SIAM J. Appl. Math., 50, pp. 918-930. , Zbl 0717.35092 MR 1050922
  • Del Pezzo, L.M., Mosquera, C.A., Rossi, J.D., Estimates for nonlinear harmonic measures on trees (2013), Preprint. arXiv:1303.6521; Kaufman, R., Llorente, J.G., Wu, J.-M., Nonlinear harmonic measures on trees (2003) Ann. Acad. Sci. Fenn. Math., 28, pp. 279-302. , Zbl 1033.31004 MR 1996439
  • Kaufman, R., Wu, J.-M., Fatou theorem of p-harmonic functions on trees (2000) Ann. Probab., 28, pp. 1138-1148. , Zbl 1038.31007 MR 1797306
  • Manfredi, J.J., Oberman, A., Sviridov, A., Nonlinear elliptic PDEs and p-harmonic functions on graphs (2012), Preprint. arXiv:1212.0834; Sviridov, A.P., Elliptic equations in graphs via stochastic games (2011), http://d-scholarship.pitt.edu/9581/, Ph.D. thesis, University of Pittsburgh, Pittsburgh; Sviridov, A.P., P-harmonious functions with drift on graphs via games (2011) Electron. J. Differential Equations, p. 114. , Zbl 1229.35304 MR 2836795
  • Weber, A., Analysis of the physical Laplacian and the heat flow on a locally finite graph (2010) J. Math. Anal. Appl., 370, pp. 146-158. , Zbl 1214.35075 MR 2651136
  • Wojciechowski, R.K., Heat kernel and essential spectrum of infinite graphs (2009) Indiana Univ. Math. J, 58, pp. 1419-1441. , Zbl 1231.05186 MR 2542093

Citas:

---------- APA ----------
Del Pezzo, L.M., Mosquera, C.A. & Rossi, J.D. (2014) . Existence, uniqueness and decay rates for evolution equations on trees. Portugaliae Mathematica, 71(1), 63-77.
http://dx.doi.org/10.4171/PM/1941
---------- CHICAGO ----------
Del Pezzo, L.M., Mosquera, C.A., Rossi, J.D. "Existence, uniqueness and decay rates for evolution equations on trees" . Portugaliae Mathematica 71, no. 1 (2014) : 63-77.
http://dx.doi.org/10.4171/PM/1941
---------- MLA ----------
Del Pezzo, L.M., Mosquera, C.A., Rossi, J.D. "Existence, uniqueness and decay rates for evolution equations on trees" . Portugaliae Mathematica, vol. 71, no. 1, 2014, pp. 63-77.
http://dx.doi.org/10.4171/PM/1941
---------- VANCOUVER ----------
Del Pezzo, L.M., Mosquera, C.A., Rossi, J.D. Existence, uniqueness and decay rates for evolution equations on trees. Port. Math. 2014;71(1):63-77.
http://dx.doi.org/10.4171/PM/1941