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Dirichlet‐to‐Neumann Map for a Nonlinear Diffusion Equation
Author(s) -
Barone Vincenzo,
De Lillo Silvana,
Lupo Gaia,
Polimeno Antonino
Publication year - 2011
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2010.00500.x
Subject(s) - uniqueness , mathematics , neumann boundary condition , mathematical analysis , dirichlet distribution , boundary value problem , contraction mapping , dirichlet boundary condition , nonlinear system , contraction (grammar) , fixed point theorem , physics , medicine , quantum mechanics
A nonlinear diffusive equation with moving boundaries is analyzed by constructing the corresponding Dirichlet‐to‐Neumann map. In particular, the Dirichlet boundary value and the initial condition are used to derive the unknown Neumann boundary value. Then, a contraction‐mapping technique is used to prove existence and uniqueness of the solution for small times.