ASYMPTOTICS OF THE SOLUTION OF THE FIRST BOUNDARY VALUE PROBLEM FOR A SINGULARLY PERTURBED DIFFERENTIAL EQUATION IN PARTIAL DERIVATIVES OF THE SECOND ORDER OF PARABOLIC TYPE

The article constructs a complete uniform asymptotic expansion in small parameter of the solution first boundary value problem. problem is posed for singularly perturbed linear inhomogeneous second-order partial differential equation with two independent variables parabolic type. investigated on rectangle. peculiarities are presence front heat conduction operator, existence corner layers at lower corners It required to construct rectangle, any degree accuracy, as tends zero. terms constructed by Vishik–Lyusternik method. When solving problem, we use: methods integration ordinary equations, classical method parameter, function method, and maximum principle. As usual, solved stages: stage, formal constructed; second remainder resulting estimated this proves that indeed over entire In sought form sum six functions (solutions): an external defined rectangle; layer neighborhood side lateral solutions sides rectangle vertices All these exponentially decrease outside layers.