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.
"On Solutions of First Order PDE with Two-Dimensional Dirac Delta Forcing Terms,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 24:
2, Article 2.
Available at: https://scholar.rose-hulman.edu/rhumj/vol24/iss2/2