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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.

Solvability of degenerated parabolic equations without sign condition and three unbounded nonlinearities.

Akdim, Youssef, Bennouna, Jaouad, Mekkour, Mounir (2011)

Electronic Journal of Differential Equations (EJDE) [electronic only]

The finite speed of propagation of solutions of the Neumann problem of a degenerate parabolic equation

Jiaqing Pan (2011)

Open Mathematics

In this paper the finite speed of propagation of solutions and the continuous dependence on the nonlinearity of a degenerate parabolic partial differential equation are discussed. Our objective is to derive an explicit expression for the speed of propagation and the large time behavior of the solution and to show that the solution continuously depends on the nonlinearity of the equation.

Displaying 21 – 23 of 23

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

Solvability of degenerated parabolic equations without sign condition and three unbounded nonlinearities.

The finite speed of propagation of solutions of the Neumann problem of a degenerate parabolic equation

Currently displaying 21 – 23 of 23