Ill-posed fuzzy initial-boundary value problems based on generalized differentiability and regularization

In this study, based on a new generalized differentiability and parametric representation for fuzzy valued functions, we discuss the existence of solutions for fuzzy partial differential equations (FPDEs) and their ill-posedness. A regularization method is required to recover the numerical stability. A stable approximation of the exact solution is obtained as an example of a Cauchy problem for the fuzzy Laplace equation.