Nonhomogeneous Boundary Value Problems

The diffusion equation is solved under stochastic nonhomogeneity using eigen function expansion and the Georges method. The statistical moments of the solution process are computed through the two previously mentioned techniques and proved to be the same. A general solution is obtained under general initial and boundary conditions. A random source composed of deterministic and stochastic parts is taken into consideration. The stochastic part is then restricted to a generalized Gaussian field, mainly modulated white noise. A special case is considered under constant noise level and constant average noise. A numerical case study concerning pollution in a stream is solved and a parametric study is achieved through various figures