caa a22 4500 467891133 CHVBK 20180406152749.0 cr unu---uuuuu 170328e20060701xx s 000 0 eng 10.1007/s10955-006-9136-5 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9136-5 Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential [Elektronische Daten] [N. Leonenko, M. Ruiz-Medina] The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329-4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios. Springer Science + Business Media, Inc., 2006 nonhomogeneous multidimensional Burgers equation nationallicence quadratic external potential nationallicence scaling laws nationallicence spatiotemporal random fields nationallicence strongly dependent random initial conditions nationallicence Leonenko N. Cardiff School of Mathematics, Cardiff University, Senghennydd Road, CF24 4AG, Cardiff, United Kingdom aut Ruiz-Medina M. Department of Statistics and Operations Research, University of Granada, Campus de Fuente Nueva s/n, E-18071, Granada, Spain aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/1(2006-07-01), 191-205 0022-4715 124:1<191 2006 124 10955 https://doi.org/10.1007/s10955-006-9136-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9136-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Leonenko N. Cardiff School of Mathematics, Cardiff University, Senghennydd Road, CF24 4AG, Cardiff, United Kingdom aut NATIONALLICENCE 700 1- Ruiz-Medina M. Department of Statistics and Operations Research, University of Granada, Campus de Fuente Nueva s/n, E-18071, Granada, Spain aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/1(2006-07-01), 191-205 0022-4715 124:1<191 2006 124 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer