The-time dependent thin obstacle problem for the weighted bi-Laplacian

Abstract: Time dependent equations associated with fourth order operators are used to model many physical phenomena such as plane flame propagation, and phase turbulence in reaction-diffusion systems. They also appears in thin film theory to model long waves on a viscous fluid. We will present our work on a time dependent thin obstacle problem associated with the weighted bi-Laplace operator. We study the well-posedness of the problem and the regularity of the solution. Our approach is based on an implicit time discretization method.

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