On local solvability of linear partial differential equations

On Local Solvability of Linear Partial Differential Equations

The title indicates more or less what the talk is going to be about. I t is going to be about the problem which is probably the most primitive in partial differential equations theory, namely to know whether an equation does, or does not, have a solution. Even this is meant in the most primitive terms. I would like to begin by explaining what the terms are. As you all know, the really difficult...

Numerical Linear Algebra and Solvability of Partial Differential Equations

On d-solvability for linear differential equations

The aim of this paper is to investigate the possibility of solving a linear differential equation of degree n by means of differential equations of degree less than or equal to a fixed d, 1 ≤ d < n. This paper recovers and extends work of G. Fano, M. F. Singer and E. Compoint. Representations of algebraic Lie algebras are themain tool. © 2008 Elsevier Ltd. All rights reserved.

P.R. Popivanov LOCAL SOLVABILITY OF SOME CLASSES OF LINEAR AND NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

The paper deals with the local nonsolvability of several examples of linear and nonlinear partial differential equations. In the linear case we prove nonsolvability in Schwartz distribution space while in the nonlinear case we prove the nonexistence of classical solutions as well as the nonexistence of L∞ ∩ H s , s > 0, solutions. 1. This paper deals with the local nonsolvability of several exa...

Exact Solution for Nonlinear Local Fractional Partial Differential Equations

In this work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Then, we apply this new algorithm to resolve the nonlinear local fractional gas dynamics equation and nonlinear local fractional Klein-Gordon equation, so we get the desired non-differentiable exact solutions. The steps to solve the examples a...