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Semi-analytical approach to initial problems for systems of nonlinear partial differential equations with constant delay

Šamajová, Helena (2017)

Proceedings of Equadiff 14

This paper deals with the differential transform method for solving of an initial value problem for a system of two nonlinear functional partial differential equations of parabolic type. We consider non-delayed as well as delayed types of coupling and the different variety of initial functions are thought over. The convergence of solutions and the error estimation to the presented procedure is studied. Two numerical examples for non-delayed and delayed systems are included.

Solvability of a class of phase field systems related to a sliding mode control problem

Michele Colturato (2016)

Applications of Mathematics

We consider a phase-field system of Caginalp type perturbed by the presence of an additional maximal monotone nonlinearity. Such a system arises from a recent study of a sliding mode control problem. We prove the existence of strong solutions. Moreover, under further assumptions, we show the continuous dependence on the initial data and the uniqueness of the solution.

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