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On Solutions Of First Order Pde With Two-Dimensional Dirac Delta Forcing Terms, Ian Robinson
On Solutions Of First Order Pde With Two-Dimensional Dirac Delta Forcing Terms, Ian Robinson
Rose-Hulman Undergraduate Mathematics Journal
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.