2023-12-01T10:52:00Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/421662023-08-27T19:00:57Zcom_20.500.14352_14col_20.500.14352_15
Lagrangian approach to the study of level sets II: A quasilinear equation in climatology
Díaz Díaz, Jesús Ildefonso
Shmarev, Sergey
We study the dynamics and regularity of the level sets in solutions of the semilinear parabolic equation u(t) - Delta p(u) + f is an element of aH(u - mu) in Q = Omega x (0, T], P is an element of (1, infinity), where Omega subset of R(n) is a ring-shaped domain, Delta(p)u is the p-Laplace operator, a and mu are given positive constants, and H(.) is the Heaviside maximal monotone graph: H(s) = 1 if s > 0, H(0) = [0, 1], H(s) = 0 if s < 0. The mathematical models of this type arise in climatology, the case p = 3 was proposed and justified by P. Stone in 1972. We establish the conditions on the initial data which guarantee that the level sets Gamma(mu)(t) = {x: u(x, t) = mu} are hypersurfaces, study the regularity of Gamma(mu)(t) and derive the differential equation that governs the dynamics of Gamma(mu)(t). The analysis is based on the introduction of a system of Lagrangian coordinates that transforms the moving surface Gamma(mu)(t) into a stationary one.
2023-06-20T00:11:38Z
2023-06-20T00:11:38Z
2009-04-01
journal article
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0022-247X
10.1016/j.jmaa.2008.09.046
https://hdl.handle.net/20.500.14352/42166
http://www.sciencedirect.com/science/article/pii/S0022247X08009426
http://www.sciencedirect.com/
eng
MTM2005-03463
MTM2007-65088.
restricted access
Elsevier