RT Journal Article
T1 Lagrangian approach to the study of level sets II: A quasilinear equation in climatology
A1 Díaz Díaz, Jesús Ildefonso
A1 Shmarev, Sergey
AB 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.
PB Elsevier
SN 0022-247X
YR 2009
FD 2009-04-01
LK https://hdl.handle.net/20.500.14352/42166
UL https://hdl.handle.net/20.500.14352/42166
LA eng
NO DGISGPI
DS Docta Complutense
RD 12 abr 2025