Abstract
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.
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