A stochastic half-space problem in the theory of generalized thermoelastic diffusion including heat source

A stochastic half-space problem, driven by an additive Gaussian white noise, is considered within the context of the theory of generalized thermoelastic diffusion with one relaxation time. The bounding surface is traction free and subjected to a time dependent thermal shock. A permeating substance is considered in contact with the bounding surface. Laplace transform technique is used to obtain the solution in the transformed domain by using a direct approach. The mean and variance are derived and analyzed for temperature, displacement, stress, strain, concentration and chemical potential. The asymptotic behavior for the solution is discussed. Numerical results are carried out and represented graphically. The second sound effect is observed in the simulation.