In this paper, we prove the existence of solutions for a class of viscoelastic dynamic systems on time-dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions we also show a uniqueness result. Finally, we exhibit an example where the energy-dissipation balance is not satisfied, showing there is an additional dissipation due to the crack growth.

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To comply with stringent NO x emission regulations, automotive diesel engines require advanced aftertreatment catalytic systems, such as lean NO x traps (LNTs). Considering that test bench and chassis dyno experimental campaigns are costly and require a vast use of resources for the generation of data; therefore, reliable and computationally efficient simulation models are essential in order to identify the most promising technology mix to satisfy emission regulations. In the literature, a large number of simulation models for LNT kinetics can be found, realized for laboratory-scale samples and validated over synthetic gas bench (SGB) experimental tests, while full-size models validated over engine-dyno driving cycle data, crucial for industrial applications, are missing. In the current work, a simulation model of an LNT device is built to predict NO x storage and reduction, starting from SGB laboratory tests and finally validated over driving cycle data. The experiments including light-off, NO x storage and reduction (NSR), and oxygen storage capacity (OSC) characterization, were performed on a laboratory-scale sample extracted from a full-scale monolith. Light-off tests have been conducted under a temperature ramp cycle from 120 °C to 380 °C, while OSC and NSR tests were performed under isothermal conditions at five temperature levels, ranging from 150 °C to 400 °C. OSC tests were performed to characterize oxygen storage capacity of ceria sites and water gas shift (WGS) reaction over the precious metals by controlling inlet species concentrations with periodic lean/rich pulses. NSR experiments were then performed by alternating a lean inlet composition to reproduce adsorption/desorption of NO x with a rich inlet composition feed with three reductants (H 2 , CO, and C 3 H 6 ) to replicate NO x reduction reactions. A global kinetic scheme was defined by means of a one-dimensional (1D) engine simulation fluid-dynamic code, GT-SUITE, to model oxidation reactions (CO, HC, NO), NO x adsorption/desorption, oxygen storage and NO x reduction reactions. The kinetic parameters were obtained using Arrhenius plots with the aim to minimize the error between simulated and experimental NO x , reductants, N 2 O and NH 3 concentrations, reaching a satisfactory agreement with measurements.

We prove an existence result for the fractional Kelvin–Voigt’s model involving Caputo’s derivative on time-dependent cracked domains. We first show the existence of a solution to a regularized version of this problem. Then, we use a compactness argument to derive that the fractional Kelvin–Voigt’s model admits a solution which satisfies an energy-dissipation inequality. Finally, we prove that when the crack is not moving, the solution is unique.