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Award ID contains: 2006372

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  1. ; (, Nonlinearity)
    Abstract We derive a PDE that models the behavior of a boundary layer solution to the incompressible porous media (IPM) equation posed on the 2D periodic half-plane. This 1D IPM model is a transport equation with a non-local velocity similar to the well-known Córdoba–Córdoba–Fontelos (CCF) equation. We discuss how this modification of the CCF equation can be regarded as a reasonable model for solutions to the IPM equation. Working in the class of bounded smooth periodic data, we then show local well-posedness for the 1D IPM model as well as finite time blow-up for a class of initial data. 
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    Free, publicly-accessible full text available April 29, 2026
  2. ; (, Journal of Biological Dynamics)
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  3. ; ; ; (, Journal of the European Mathematical Society)
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  4. ; (, Archive for Rational Mechanics and Analysis)
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  5. ; (, Journal of Nonlinear Science)
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  6. ; (, Archive for Rational Mechanics and Analysis)
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  7. ; (, Annals of PDE)
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  8. ; (, Nonlinearity)
    Abstract We consider absorbing chemical reactions in a fluid flow modelled by the coupled advection–reaction–diffusion equations. In these systems, the interplay between chemical diffusion and fluid transportation causes the enhanced dissipation phenomenon. We show that the enhanced dissipation time scale, together with the reaction coupling strength, determines the characteristic time scale of the reaction. 
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  9. ; ; (, Bulletin of Mathematical Biology)
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  10. ; (, SIAM Journal on Mathematical Analysis)
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