Applications of Partial Differential Equation & Relation with Fourier

In this work, when modeling problems over regions that extended very far in at least one direction, we often idealized the situation to that of a problem having infinite extent in one or more directions, where any boundary conditions that would have applied on the far-away boundaries are discarded in favor of simple bounded-ness conditions on the solution as the appropriate variable is sent to infinity. Such problems were mathematically modeled by differential equations defined on infinite regions. For one-dimensional problems we distinguish two types of infinite regions: infinite intervals extending from -¿ to ¿ and semi-infinite intervals extending from one point (usually the origin) to infinite (usually + ¿) are infinite, but by introducing a mathematical model with infinite extent, we are able to determine behavior of problems in the situations in which the influence of actual boundaries are expected to be negligible.