Overdetermined Systems of Linear Partial Differential Operators with Normal Principal Symbols

On the Numerical Analysis of Overdetermined Linear Partial Differential Systems

We discuss the use of the formal theory of differential equations in the numerical analysis of general systems of partial differential equations. This theory provides us with a very powerful and natural framework for generalising many ideas from differential algebraic equations to partial differential equations. We study in particular the existence and uniqueness of (formal) solutions, the meth...

Exact and numerical solutions of linear and non-linear systems of fractional partial differential equations

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

Multiplication of solutions for linear overdetermined systems of partial differential equations

A large family of linear, usually overdetermined, systems of partial differential equations that admit a multiplication of solutions, i.e, a bilinear and commutative mapping on the solution space, is studied. This family of PDE’s contains the Cauchy–Riemann equations and the cofactor pair systems, included as special cases. The multiplication provides a method for generating, in a pure algebrai...

On the Principal Symbols of Kc-invariant Differential Operators on Hermitian Symmetric Spaces

Let (G, K) be one of the following classical irreducible Hermitian symmetric pairs of noncompact type: (SU(p, q), S (U(p) × U(q))), (Sp(n,R),U(n)), or (SO(2n),U(n)). Let GC and KC be complexifications of G and K, respectively, and let P be a maximal parabolic subgroup of GC whose Levi subgroup is KC. Let V be the holomorphic part of the complexifiaction of the tangent space at the origin of G/K...

Linear Operators in the Theory of Partial Differential Equations