Title

On Solutions of First Order PDE with Two-Dimensional Dirac Delta Forcing Terms

Presenter Information

Ian RobinsonFollow

Academic Level at Time of Presentation

Senior

Major

Mathematics/Secondary Education Area

List all Project Mentors & Advisor(s)

Justin Taylor, PhD.

Presentation Format

Oral Presentation

Abstract/Description

This presentation will be a review of my research in PDE Theory. The goal of this work is to provide solutions of a first order, linear partial differential equation of two variables, one of space and one of time, where the nonhomogeneous term takes the form of a two-dimensional Dirac delta function. The main results are achieved by applying the unilateral Laplace Transform with respect to the time or space variable, solving the subsequently transformed PDE, and reverting back to the original space-time domain. A discussion of uniqueness and existence of solutions, a derivation of solutions of the PDE coupled with a boundary and initial condition, as well as a few worked examples are provided.

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On Solutions of First Order PDE with Two-Dimensional Dirac Delta Forcing Terms

This presentation will be a review of my research in PDE Theory. The goal of this work is to provide solutions of a first order, linear partial differential equation of two variables, one of space and one of time, where the nonhomogeneous term takes the form of a two-dimensional Dirac delta function. The main results are achieved by applying the unilateral Laplace Transform with respect to the time or space variable, solving the subsequently transformed PDE, and reverting back to the original space-time domain. A discussion of uniqueness and existence of solutions, a derivation of solutions of the PDE coupled with a boundary and initial condition, as well as a few worked examples are provided.