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The wave equation with boundary source term and fractional boundary dissipation is considered.
We will consider the blowup of the solution for problem (1.1)–(1.4) with nonlinear boundary source term.
Then, the use of the generalized Hooke's law leads to the integral representation of stresses for a boundary source point.
Int J Solids Struct 2000 37 6623 6634, Mukherjee S. Finite parts of singular and hypersingular integrals with irregular boundary source points.
Based on the models and multi-dimensional scaling, a multi-dimensional coupling simulation method for shrouded turbines is developed, in which, some boundary source and sink are set on the interface between the shroud and the main flow passage.
Following the work of other authors, the laser source may be represented as an equivalent elastic boundary source consisting of distributed normal and shear loading on the plate surface as Eq. (15).
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This approximate boundary integral technique is based upon the integral representation for scattered elastic waves using single-layer boundary sources.
From the strong or weak satisfaction of boundary conditions and a simple analytical discretization scheme a linear system of equations for the boundary sources is obtained.
The unknown functions (the displacement of the plate, the pressure jump at the surface of the plate and the boundary sources) are expanded as series of Tchebycheff polynomials.
Based on these observations, equations for the evolution of mobile and forest dislocation densities are posed, depicting boundary sources and dislocation dislocation interactions, respectively.
There have been many kinds of extensions of Fujita's results since then, such as different types of parabolic equations and systems with or without degeneracies or singularities, various geometries of domains, different nonlinear reactions or nonhomogeneous boundary sources, etc.
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