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The paper deals with a boundary value problem governed by a nonlinear damped wave equation. It generalizes the equation modeling cerebral activity that has been proposed by Jirsa and Haken [Phys, Rev. Let. 77: 960–963, 1996]. Using a Galerkin approximation scheme, we prove existence of global solutions. In the 1D case, we show the continuous dependence of solutions with respect to initial data and derive uniqueness.

On solutions of a nonlinear wave equation derived from brain activity modeling