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Partial Differential Equations Commons™

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2022

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Articles 31 - 33 of 33

Full-Text Articles in Partial Differential Equations

Existence And Uniqueness Of Minimizers For A Nonlocal Variational Problem, Michael Pieper Mar 2022

Existence And Uniqueness Of Minimizers For A Nonlocal Variational Problem, Michael Pieper

Honors Program: Senior Projects (Public)

Nonlocal modeling is a rapidly growing field, with a vast array of applications and connections to questions in pure math. One goal of this work is to present an approachable introduction to the field and an invitation to the reader to explore it more deeply. In particular, we explore connections between nonlocal operators and classical problems in the calculus of variations. Using a well-known approach, known simply as The Direct Method, we establish well-posedness for a class of variational problems involving a nonlocal first-order differential operator. Some simple numerical experiments demonstrate the behavior of these problems for specific choices of …


Inverse Boundary Value Problems For Polyharmonic Operators With Non-Smooth Coefficients, Landon Gauthier Jan 2022

Inverse Boundary Value Problems For Polyharmonic Operators With Non-Smooth Coefficients, Landon Gauthier

Theses and Dissertations--Mathematics

We consider inverse boundary problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity required to establish uniqueness. The proof relies on an averaging technique introduced by Haberman and Tataru for the study of an inverse boundary value problem for a second order operator.


Towards Simulation Of Complex Ocean Flows: Analysis And Algorithm For Computation Of Coupled Partial Differential Equations, Wenbin Dong Jan 2022

Towards Simulation Of Complex Ocean Flows: Analysis And Algorithm For Computation Of Coupled Partial Differential Equations, Wenbin Dong

Dissertations and Theses

The hybrid CFD models which usually consist of 2 sub-models, develop our capability to simulate many emerging problems with multiphysics and multiscale flows, especially for the coastal ocean flows interacted with local phenomena of interest. For most cases, the sub-models are connected with direct interpolation which is easy and workable. It becomes urgently needed to investigate the inner mechanism of such model integration as this simple method does not work well if the two sub-models are different in governing equations, numerical methods, and computational grids. Also, it can not treat complex flow structures as well as the balance in mass …