skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 2

Search for: All records

Award ID contains: 2204288

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; (, European Journal of Applied Mathematics)
    Abstract We prove the convergence of a Wasserstein gradient flow of a free energy in inhomogeneous media. Both the energy and media can depend on the spatial variable in a fast oscillatory manner. In particular, we show that the gradient-flow structure is preserved in the limit, which is expressed in terms of an effective energy and Wasserstein metric. The gradient flow and its limiting behavior are analysed through an energy dissipation inequality. The result is consistent with asymptotic analysis in the realm of homogenisation. However, we note that the effective metric is in general different from that obtained from the Gromov–Hausdorff convergence of metric spaces. We apply our framework to a linear Fokker–Planck equation, but we believe the approach is robust enough to be applicable in a broader context. 
    more » « less
    Free, publicly-accessible full text available July 29, 2026
  2. ; (, Nonlinearity)
    Abstract We study the existence and uniqueness of solutions to the vector field Peierls–Nabarro (PN) model for curved dislocations in a transversely isotropic medium. Under suitable assumptions for the misfit potential on the slip plane, we reduce the 3D PN model to a nonlocal scalar Ginzburg–Landau equation. For a particular range of elastic coefficients, the nonlocal scalar equation with explicit nonlocal positive kernel is derived. We prove that any stable steady solution has a one-dimensional profile. As a result, we obtain that solutions to the scalar equation, as well as the original 3D system, are characterized as a one-parameter family of straight dislocations. This paper generalizes results found previously for the full isotropic case to an anisotropic setting. 
    more » « less
    Full Text Available 
  3. ; ; (, Advances in Calculus of Variations)
    Abstract We study the following parabolic nonlocal 4-th order degenerate equation arising from the epitaxial growth on crystalline materials. Here a>0 is a given parameter. By relying on the theory of gradient flows,we first prove the global existence of a variational inequality solution with a general initial datum.Furthermore, to obtain a global strong solution, the main difficulty is the singularity of the logarithmic term when {u_{xx}+a} approaches zero. Thus we show that,if the initial datum is uniformly bounded away from zero,then such property is preserved for all positive times.Finally, we will prove several higher regularity results for this global strong solution.These finer properties provide a rigorous justification for the global-in-time monotone solution to the epitaxial growth model with nonlocal elastic effects on vicinal surface. 
    more » « less
    Full Text Available 
  4. ; (, SIAM/ASA Journal on Uncertainty Quantification)
    Free, publicly-accessible full text available December 31, 2026
  5. ; (, Journal of differential equations)
    Free, publicly-accessible full text available December 25, 2026
  6. ; ; (, Acta Applicandae Mathematicae)
    Full Text Available 
  7. ; ; (, Journal of Scientific Computing)
    Full Text Available 
  8. ; ; (, Discrete and Continuous Dynamical Systems - B)
    Full Text Available 
  9. ; (, SIAM Journal on Mathematical Analysis)
    Full Text Available 
  10. ; (, Multiscale Modeling & Simulation)
    Full Text Available