### Abstract

We consider a reaction-difiusion equation for the front motion u in which the reaction term is given by c(x)g(u). We formulate a suitable inverse problem for the unknowns u and c, where u satisfies homogeneous Neumann boundary conditions and the additional condition is of integral type on the time interval [0; T]. Uniqueness of the solution is proved in the case of a linear g. Assuming g non linear, we show uniqueness for large T.

Original language | English (US) |
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Pages (from-to) | 285-296 |

Number of pages | 12 |

Journal | Inverse Problems and Imaging |

Volume | 5 |

Issue number | 2 |

DOIs | |

State | Published - May 1 2011 |

### Fingerprint

### Keywords

- Inverse problems
- Reaction-difiusion equations

### ASJC Scopus subject areas

- Analysis
- Modeling and Simulation
- Discrete Mathematics and Combinatorics
- Control and Optimization

### Cite this

*Inverse Problems and Imaging*,

*5*(2), 285-296. https://doi.org/10.3934/ipi.2011.5.285

**Identifying a space dependent coefficient in a reaction-diffusion equation.** / Beretta, Elena; Cavaterra, Cecilia.

Research output: Contribution to journal › Article

*Inverse Problems and Imaging*, vol. 5, no. 2, pp. 285-296. https://doi.org/10.3934/ipi.2011.5.285

}

TY - JOUR

T1 - Identifying a space dependent coefficient in a reaction-diffusion equation

AU - Beretta, Elena

AU - Cavaterra, Cecilia

PY - 2011/5/1

Y1 - 2011/5/1

N2 - We consider a reaction-difiusion equation for the front motion u in which the reaction term is given by c(x)g(u). We formulate a suitable inverse problem for the unknowns u and c, where u satisfies homogeneous Neumann boundary conditions and the additional condition is of integral type on the time interval [0; T]. Uniqueness of the solution is proved in the case of a linear g. Assuming g non linear, we show uniqueness for large T.

AB - We consider a reaction-difiusion equation for the front motion u in which the reaction term is given by c(x)g(u). We formulate a suitable inverse problem for the unknowns u and c, where u satisfies homogeneous Neumann boundary conditions and the additional condition is of integral type on the time interval [0; T]. Uniqueness of the solution is proved in the case of a linear g. Assuming g non linear, we show uniqueness for large T.

KW - Inverse problems

KW - Reaction-difiusion equations

UR - http://www.scopus.com/inward/record.url?scp=79958042909&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79958042909&partnerID=8YFLogxK

U2 - 10.3934/ipi.2011.5.285

DO - 10.3934/ipi.2011.5.285

M3 - Article

AN - SCOPUS:79958042909

VL - 5

SP - 285

EP - 296

JO - Inverse Problems and Imaging

JF - Inverse Problems and Imaging

SN - 1930-8337

IS - 2

ER -