Siam Journal on Applied Mathematics

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We build and analyze a mathematical model of a system for biogas upgrading: an absorption column connected to a microalgae culture. The construction of the model is based on a chemical engineering approach and classical models of microalgae cultures. In our analysis, we prove the existence and uniqueness of solutions of a boundary value problem describing the absorption column. Some properties of this solution are also proved. Then, we use these results to study the long-term behavior of the mat...

The classical dam-break problem for the shallow water system with a dry/vacuum downstream state is revisited in the context of exact solutions which generalize the Riemann setup of a Heaviside jump...

A common form of superhydrophobic surface is made out of a periodically grooved solid substrate, wherein cylindrical bubbles are trapped in a Cassie state. When a macroscopic temperature gradient i...

The deformation and stability of a two-dimensional inextensible elastic cell in an inviscid uniform stream are investigated using a conformal mapping method. At low flow speeds equilibrium solutions are obtained using an asymptotic expansion, and the sequence of critical dimensionless pressures identified by Flaherty et al. (1972) for a circular cell exposed to a uniform transmural pressure is shown to play a crucial role. Below the smallest critical pressure a circular cell in a weak flow defor...

On the Convergence of a Regularization Scheme for Approximating Cavitation Solutions with Prescribed Cavity Volume

Let \Omega\in\mathbb{R}^n n=2,3 be the region occupied by a hyperelastic body in its reference configuration. Let E(\cdot)be the stored energy functional, and let x_0be a flaw point in ...

We consider a model that describes a flow of a thin liquid film modified by insoluble surfactant which is moving down a slope. For this model, parameter regimes were previously identified when the ...

The well-studied selection problems involving Saffman--Taylor fingers or Taylor--Saffman bubbles in a Hele-Shaw channel are prototypical examples of pattern selection. Exact solutions to the corres...

We investigate a recently proposed cross-diffusion system modeling the growth of gliobastoma taking into account size exclusion in both the migration and the proliferation process. In addition to d...

In this paper, we give a systematic stability analysis of the quadrature-based moment method (QBMM) for the one-dimensional Boltzmann equation with BGK or Shakhov models. As reported in recent lite...

The thermal interaction between adjacent boreholes plays a fundamental role in the long-term thermal response of geothermal heat exchangers. When approximating the long-term behavior by a time-peri...

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