RT Journal Article
T1 Mathematical analysis of a parabolic-elliptic problem with moving parabolic subdomain through a Lagrangian approach
A1 Muñoz Sola, Rafael
K1 Parabolic-elliptic problem
K1 Moving parabolic subdomain
K1 Regularity
K1 Lagrangian formulation
AB The aim of this paper is to study the regularity of the solution of some linear parabolic-elliptic problems in which parabolicity region depends on time. More specifically, this region is the position occupied by a body undergoing a motion (a deformation smoothly evolving in time). The main tool we introduce is a suitable extension of the motion to the entire spatial domain of the PDE. This enables us to reduce the original problem to a parabolic-elliptic problem with variable coefficients and with a parabolicity region independent of time. This problem can be seen as a Lagrangian formulation of our original problem. Next, we obtain regularity results for a class of parabolic-elliptic problems with variable coefficients and fixed parabolicity region. We apply these results to the Lagrangian formulation and, finally, we obtain a regularity result for our original problem.
PB Elsevier
SN 1096-0813
YR 2019
FD 2019
LK https://hdl.handle.net/10347/40790
UL https://hdl.handle.net/10347/40790
LA eng
NO Muñoz-Sola, R. (2019). Mathematical analysis of a parabolic-elliptic problem with moving parabolic subdomain through a Lagrangian approach. Journal of Mathematical Analysis and Applications, 477(1), 357-379. https://doi.org/10.1016/J.JMAA.2019.04.035
NO This work has been partially supported by FEDER/Ministerio de Ciencia, Innovación y Universidades – Agencia Estatal de Investigación under the research project MTM2017-86459-R and Xunta de Galicia (Spain) under grant 2017 GRC GI-1563. Thanks are also given to the anonymous referee for some helpful suggestions.
DS Minerva
RD 28 abr 2026