Complex transformations of solutions of cauchy problems with application

Abstract

Transformations that connect solutions of higher order Cauchy problems to corresponding lower order ones are examined. These generally have a non-transmutational character. They are employed to study the limiting behaviors of solutions of various Euler-PoissonDarboux type problems relative to parameters appearing in the underlying equations and to solve Cauchy problems that involve iterated operators. Consideration is also given to higher order systems of partial differential equations.

Keywords:

• Cauchy problems
• quasi inner product
• transformations
• Eule-Poisson-Darboux type problems
• iterated operators
• systems of equations