Abstract
Many linear partial differential equations in mathematical physics have the fundamental solutions with singularities. This does not correspond to the real physical situation. The additional terms were introduced into the classical equations using the constitutive laws for internal body interactions and so the MAC models were created. This paper analyzes the boundedness of the fundamental solutions of some MAC models with local internal body forces. The 1D, 2D, and 3D steady state problems are considered. The mechanical models are an elastic string, heat conduction, membrane, plate, linear isotropic elasticity. The Fourier transform is used. The new strength criteria is given. It is shown that the displacements under applied force are finite for membrane, plate and in 2D and 3D elasticity. The bending stresses are finite in plate. The stresses are zero in elasticity problem at the point of applied force but the new strength criteria is working in this case too. The temperatures are finite in case of 2D and 3D point source of heat flux.
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Neygebauer, I. (2016). Bounded and Unbounded Fundamental Solutions in MAC Models. In: Anastassiou, G., Duman, O. (eds) Computational Analysis. Springer Proceedings in Mathematics & Statistics, vol 155. Springer, Cham. https://doi.org/10.1007/978-3-319-28443-9_12
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DOI: https://doi.org/10.1007/978-3-319-28443-9_12
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