https://hal-normandie-univ.archives-ouvertes.fr/hal-02426063Hamdi, AdelAdelHamdiLMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie - INSA Rouen Normandie - Institut national des sciences appliquées Rouen Normandie - INSA - Institut National des Sciences Appliquées - NU - Normandie UniversitéMahfoudhi, ImedImedMahfoudhiLMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie - INSA Rouen Normandie - Institut national des sciences appliquées Rouen Normandie - INSA - Institut National des Sciences Appliquées - NU - Normandie UniversitéInverse source problem in a one-dimensional evolution linear transport equation with spatially varying coefficients: application to surface water pollutionHAL CCSD2013inverse source problemoptimizationpartial differential equationsadvection–dispersion–reaction equationsenvironmental monitoring: surface water pollution[MATH] Mathematics [math][MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP][MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA][MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Hamdi, Adel2020-01-01 14:39:272022-03-02 09:42:122020-01-01 14:39:27enJournal articles10.1080/17415977.2013.7648711This paper deals with the identification of a time-dependent point source occurring in the right-hand side of a one-dimensional evolution linear advection–dispersion–reaction equation. The originality of this study consists in considering the general case of transport equations with spatially varying dispersion, velocity and reaction coefficients which enables to extend the applicability of the obtained results to various areas of science and engineering. We derive a main condition on the involved spatially varying coefficients that yields identifiability of the sought source, provided its time-dependent intensity function vanishes before reaching the final monitoring time, from recording the generated state at two observation points framing the source region. Then, we establish an identification method that uses those records to determine the elements defining the sought source. Some numerical experiments on a variant of the surface water pollution model are presented.