Thermal problem of curvilinear cracks in bonded dissimilar materials with a point heat source
The special boundary value problem for the function \(\Phi(z)\) analytic on the circle \(| z|= 1\) has been solved in closed form. The circle is subdivided into two arcs, and the conditions \(\Phi^ += a \Phi^ -+ b \overline{\Phi^ -}+ c\) and \(\text{Re }\Phi^ \pm= 0\) hold on the first and on the second arc, respectively. Here \(a\) and \(b\) are given constants, \(c\) is a given function. The subscripts \(+\) and \(-\) are used to denote the boundary values of \(\Phi\) as they are approached from \(| z|< 1\) and \(| z|> 1\), respectively.
scientific article; zbMATH DE number 516586