A Laguerre expansion of the Cauchy problem for convective diffusive flow

AbstractA solution to an inverse problem involving noncharacteristic Cauchy conditions for a one-dimensional parabolic partial differential equation is presented which extends previous work in which the effects of a first-order convective term were ignored. The new solution involves a series expansion in Laguerre polynomials in time with spatial coefficients expressed in terms of a new set of special functions. These special functions are studied and many new properties are derived including a set of five term recurrence relations. The paper concludes with a theoretical study of conditions under which the inverse problem is well-posed