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Award ID contains: 2206453

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  1. ; ; (, Applied mathematical modelling)
    This survey provides a concise yet comprehensive overview on enhanced dissipation phenomena, transitioning seamlessly from the physical principles underlying the interplay between advection and diffusion to their rigorous mathematical formulation and analysis. The discussion begins with the standard theory of enhanced dissipation, highlighting key mechanisms and results, and progresses to its applications in notable nonlinear PDEs such as the Cahn-Hilliard and the Kuramoto-Sivashinsky equations. 
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    Free, publicly-accessible full text available July 24, 2026
  2. ; ; ; (, Research in the Mathematical Sciences)
    Not AvailableWe consider the inverse problem of determining an elastic dislocation that models a seismic fault in the quasi-static regime of aseismic, creeping faults, from displacement measurements made at the surface of Earth. We derive both a distributed and a boundary shape derivative that encodes the change in a misfit functional between the measured and the computed surface displacement under infinitesimal movements of the dislocation and infinitesimal changes in the slip vector, which gives the displacement jump across the dislocation. We employ the shape derivative in an iterative reconstruction algorithm. We present some numerical test of the reconstruction algorithm in a simplified 2D setting. 
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    Free, publicly-accessible full text available June 1, 2026
  3. ; (, Communications in Mathematical Sciences)
    We establish conditions for shear flows on the d -dimensional torus that give enhanced dissipation for the associated linear advection-diffusion equation for well-prepared data. The diffusion operator can be of fractional or high order and does not need to have constant coefficients. We then construct flows that satisfy these assumptions and obtain a quantitative estimate on the dissipation enhancement. Our examples generalize known examples in two space dimensions to the high-dimensional setting, which is relevant in applications to sampling a distribution and in optimization. 
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  4. ; ; (, Journal de mathématiques pures et appliquées)
    The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. We establish well-posedness with inflow, outflow of velocity when either the full value of the velocity is specified on inflow, or only the normal component is specified along with the vorticity (and an additional constraint). We derive compatibility conditions to obtain regularity in a Hölder space with prescribed arbitrary index, and allow multiply connected domains. Our results apply as well to impermeable boundaries, establishing higher regularity of solutions in Hölder spaces. 
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  5. ; ; ; (, Notices of the American Mathematical Society)
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  6. ; ; (, Physica D: Nonlinear Phenomena)
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