Well-posedness of initial value problems for singular parabolic equations

Initial - Boundary Value Problems for Parabolic Equations

Well-Posedness of Initial Value Problems for Functional Differential and Algebraic Equations of Mixed Type

We study the well-posedness of initial value problems for scalar functional algebraic and differential functional equations of mixed type. We provide a practical way to determine whether such problems admit unique solutions that grow at a specified rate. In particular, we exploit the fact that the answer to such questions is encoded in an integer n. We show how this number can be tracked as a p...

WELL- POSEDNESS OF THE ROTHE DIFFERENCE SCHEME FOR REVERSE PARABOLIC EQUATIONS

Well-posedness of hyperbolic Initial Boundary Value Problems

Assuming that a hyperbolic initial boundary value problem satsifies an a priori energy estimate with a loss of one tangential derivative, we show a well-posedness result in the sense of Hadamard. The coefficients are assumed to have only finite smoothness in view of applications to nonlinear problems. This shows that the weak Lopatinskii condition is roughly sufficient to ensure well-posedness ...

Initial value problems for second order hybrid fuzzy differential equations

Usage of fuzzy differential equations (FDEs) is a natural way to model dynamical systems under possibilistic uncertainty. We consider second order hybrid fuzzy differentia