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.
Dirichlet-to-Neumann Map for a Nonlinear Diffusion Equation
POLIMENO, ANTONINO
2011
Abstract
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.File in questo prodotto:
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