Solvability of forward–backward stochastic partial differential equations

Stochastic 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...

Solvability of partial differential equations by meshless kernel methods

This paper first provides a common framework for partial differential equation problems in both strong and weak form by rewriting them as generalized interpolation problems. Then it is proven that any well–posed linear problem in strong or weak form can be solved by certain meshless kernel methods to any prescribed accuracy. AMS Subject Classification: 35A25, 65N35

Characterization for the Solvability of Nonlinear Partial Differential Equations

Within the nonlinear theory of generalized functions introduced earlier by the author a number of existence and regularity results have been obtained. One of them has been the first global version of the Cauchy-Kovalevskaia theorem, which proves the existence of generalized solutions on the whole of the domain of analyticity of arbitrary analytic nonlinear PDEs. These generalized solutions are ...

Numerical Linear Algebra and Solvability of Partial Differential Equations