# Diffusion and propagation problems in some ramified domains with a fractal boundary

Yves Achdou; Christophe Sabot; Nicoletta Tchou

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

- Volume: 40, Issue: 4, page 623-652
- ISSN: 0764-583X

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topAchdou, Yves, Sabot, Christophe, and Tchou, Nicoletta. "Diffusion and propagation problems in some ramified domains with a fractal boundary." ESAIM: Mathematical Modelling and Numerical Analysis 40.4 (2006): 623-652. <http://eudml.org/doc/249734>.

@article{Achdou2006,

abstract = {
This paper is devoted to some elliptic boundary value problems in a self-similar ramified domain of $\{\mathbb R\}^2$
with a fractal boundary. Both the Laplace and Helmholtz equations are studied. A generalized Neumann boundary condition is imposed on the fractal boundary.
Sobolev spaces on this domain are studied. In particular, extension and trace results are obtained.
These results enable the investigation of the variational formulation of the above mentioned boundary value problems. Next, for homogeneous Neumann conditions, the emphasis is placed on transparent boundary conditions, which allow the computation
of the solutions in the subdomains obtained by stopping the geometric construction after a finite number of steps. The proposed methods and algorithms
will be used numerically in forecoming papers.
},

author = {Achdou, Yves, Sabot, Christophe, Tchou, Nicoletta},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Domains with fractal boundaries; Helmholtz equation; Neumann boundary conditions; transparent boundary conditions.; elliptic boundary value problems; Neumann and transparent boundary conditions; Poisson equation; Laplace equation},

language = {eng},

month = {11},

number = {4},

pages = {623-652},

publisher = {EDP Sciences},

title = {Diffusion and propagation problems in some ramified domains with a fractal boundary},

url = {http://eudml.org/doc/249734},

volume = {40},

year = {2006},

}

TY - JOUR

AU - Achdou, Yves

AU - Sabot, Christophe

AU - Tchou, Nicoletta

TI - Diffusion and propagation problems in some ramified domains with a fractal boundary

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2006/11//

PB - EDP Sciences

VL - 40

IS - 4

SP - 623

EP - 652

AB -
This paper is devoted to some elliptic boundary value problems in a self-similar ramified domain of ${\mathbb R}^2$
with a fractal boundary. Both the Laplace and Helmholtz equations are studied. A generalized Neumann boundary condition is imposed on the fractal boundary.
Sobolev spaces on this domain are studied. In particular, extension and trace results are obtained.
These results enable the investigation of the variational formulation of the above mentioned boundary value problems. Next, for homogeneous Neumann conditions, the emphasis is placed on transparent boundary conditions, which allow the computation
of the solutions in the subdomains obtained by stopping the geometric construction after a finite number of steps. The proposed methods and algorithms
will be used numerically in forecoming papers.

LA - eng

KW - Domains with fractal boundaries; Helmholtz equation; Neumann boundary conditions; transparent boundary conditions.; elliptic boundary value problems; Neumann and transparent boundary conditions; Poisson equation; Laplace equation

UR - http://eudml.org/doc/249734

ER -

## References

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