We provide solutions of a first order, linear partial differential equation of two variables where the nonhomogeneous term is a two-dimensional Dirac delta function. Our results are achieved by applying the unilateral Laplace Transform, solving the subsequently transformed PDE, and reverting back to the original space-time domain. A discussion of existence and uniqueness 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.

Author Bio

Ian began the research detailed in "On Solutions of First Order PDE with Two-Dimensional Dirac Delta Forcing Terms" in the fall of 2021 and completed it in the fall of 2022. This work satisfied his honors thesis requirement at his undergraduate institution, Murray State University, where he majored in mathematics and secondary education. Ian is now a PhD student at the University of Kentucky and aspires to become a professor of mathematics. His favorite part of teaching is seeing his students build confidence in their math skills.