ASYMPTOTIC PROPERTIES OF PROBLEM SOLUTION ON THE STATIONARY DISTRIBUTION OF HEAT IN AN INHOMOGENIOUS PLANE WITH A CRACK
The problem considered describes the steady-state temperature distribution in heterogeneous material (FGM) with a crack. Two-dimensional case is studied. The heterogeneity of the material described by the function G(x 2) — G 0e k(cos αx1 +sin αx2 ), that corresponds to the situation of the vector direction of change of inhomogeneity is located at an angle to the positive half of abscissa axis. The problem is reduced to the generalized Cauchy problem, stationary heat potentials and solutions are built, properties are investigated. Asymptotic forms of thermal currents are obtained for the distance to the ends of the crack.