Theory of multidimensional Laplace transforms and boundary value problems
Is Version Of
In this dissertation, several theorems on multidimensional Laplace transforms are developed. These theorems are applied to most commonly used special functions to obtain many new two and three dimensional Laplace transform pairs from known one and two dimensional Laplace transforms. Last, some boundary value problems characterized by linear partial differential equations involving heat and wave equations are explicitly solved by using the obtained results to illustrate the applications.