Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Publicado
On a general type of p–adic parabolic equations
Un tipo general de ecuaciones parabólicas p–ádicas
Palabras clave:
Parabolic equations, Markov processes, p–adic numbers, ultrametric diffusion (en)Ecuaciones parabólicas, procesos de Markov, números p–ádicos, difusión ultramétrica (es)
Descargas
Abstract. In this paper we study the existence and uniqueness of the Cauchy problem for a general type of p–adic parabolic pseudo-differential operators constructed using the Taibleson operator. The results presented here constitute an extension of some results obtained by Zúñiga-Galindo and the author [13].
En este artículo se estudia la existencia y unicidad de soluciones del problema de Cauchy asociado a un tipo general de ecuación parabólica p–ádicos, construida usando el operador de Taibleson. Los resultados presentados aquí constituyen una extensión de algunos de los resultados obtenidos por Zúñiga-Galindo y el autor en [13].
Referencias
S. Albeverio and W. Karwoski, Diffusion in p–adic numbers, Gaussian Random Fields (K. Ito and H. Hida, eds.), World Scientific, Singapore, 1991, pp. 86-99.
_____, A random walk on p–adics: the generator and its spectrum, Stochastic Process. Appl. 53 (1994), 1-22.
A. V. Avetisov, A. H. Bikulov, S. V. Kozyrev, and V. A. Osipov, p–adic models of ultrametric diffusion constrained by hierarchical energy land-scapes, J. Phys. A: Math. Gen. 35 (2002), 177-189.
A. V. Avetisov, A. H. Bikulov, and V. A. Osipov, p–adic description of characteristic relaxation in complex systems, J. Phys. A: Math. Gen. 36 (2003), 4239-4246.
A. Friedman, Partial Differential Equations of the Parabolic Type, Prentice-Hall, New Jersey, 1964.
A. Yu. Khrennikov, p–adic Valued Distributions in Mathematical Physics, Kluwer, Dordrecht, 1994.
_____, Non-archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Kluwer, Dordrecht, 1997.
A. N. Kochubei, Parabolic pseudodifferential equations, hypersingular integrals, and Markov processes, Math. USSR Izvestiya 33 (1989), 233-259.
_____, Parabolic equations over the field of p –adic numbers, Math. USSR Izvestiya 39 (1992), 1263-1280.
_____, Pseudodifferential Equations and Stochastics over non-Archimedean Fields, Marcel Dekker, New York, 2001.
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type, American Mathematical Society, Providence, 1968.
R. Rammal and G. Toulouse, Ultrametricity for physicists, Rev. Modern Physics 58 (1986), 765-778.
J. J. Rodriguez-Vega and W. A. Züniga-Galindo, Taibleson operators, p –adic parabolic equations and ultrametric diffusion, Pac. Jour. Math. 237 (2008), 327-347.
M. H. Taibleson, Fourier Analysis on Local Fields, Princeton University Press, Princeton, 1975.
V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov, p –adic Analysis and Mathematical Physics, World Scientific Publishing, River Edge, NJ, 1994.
W. A. Züniga-Galindo, Parabolic equations and Markov processes over p –adic fields, Potential Analysis 28 (2008), 185-200.
