ASYMPTOTIC PROPERTIES OF PROBLEM SOLUTION ON THE STATIONARY DISTRIBUTION OF HEAT IN AN INHOMOGENEOUS 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 <i>G(x</i><sub><i>2</i></sub><i></i>) = <i>G</i><sub><i>0</i></sub><i>е</i><sup><i>kz</i></sup><i>2 </i>that corresponds to the situation of the vector direction of change of inhomogeneity is perpendicular to crack. The problem is reduced to the generalized Cauchy problem, stationary heat potentials and solutions are built, properties are investigated. Asymptotic solutions are obtained for the distance to the ends of the crack