We consider the problem of identification of a pollution source in a river. The mathematical model is a one-dimensional linear advection-dispersion-reaction equation with the right-hand side spatially supported at a point (the source) and a time-dependent intensity, both unknown. Assuming that the source becomes inactive after the time T * , we prove that it can be identified by recording the evolution of the concentration at two points, one of which is strategic.

In this work, we attempt to derive a fracture criterion for filled and unfilled elastomer vulcanizates and thermoplastics from a set of experimental data. Firstly, fracture criteria reported in the literature have been applied to experimental data obtained from tests including various loading modes (simple tension, equal biaxial tension and biaxial tension) and performed on four materials: a natural rubber (NR), a styrene butadiene rubber (SBR), a polyurethane (PU) and a thermoplastic elastomer (TPE). Then, a new failure criterion based on an equivalent elongation concept is proposed. This equivalent elongation seems to be linearly dependent on a given biaxiality ratio n=(ln(λ2b)/ln(λ1b)), which leads to expressing the principal elongations at break as functions of both the biaxiality n and two experimental parameters. Quite good agreement is highlighted when comparing the failure experimental data with the proposed criterion for the tested elastomers

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We address the nonlinear inverse source problem of identifying a time-dependent source occurring in one node of a network governed by a wave equation. We prove that time records of the associated state taken at a strategic set of two nodes yield uniqueness of the two unknown elements: the source position and the emitted signal. We develop a non-iterative identification method that localizes the source node by solving a set of well posed linear systems. Once the source node is localized, we identify the emitted signal using a deconvolution problem or a Fourier expansion. Numerical experiments on a 5 node graph confirm the effectiveness of the approach.