The Cauchy problem for the Helmholtz equation has emerged as an important yet challenging subject in applied mathematics and engineering. This problem involves deducing interior solutions from ...

This is a preview. Log in through your library . Abstract We consider a quadrature method for the Cauchy singular integral equation (CSIE): $\mathrm{a}\mathrm{\phi ...

Cauchy problems and inverse problems in partial differential equations (PDEs) represent a class of challenging mathematical models where one seeks to determine unknown data inside a domain from ...

There are three weighted decompositions of tensors proposed in this paper, and the corresponding definitions of the weighted generalized tensor functions are given. The Cauchy integral formula of the ...