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This paper is concerned with establishing global asymptotic stability results for a class of non-linear PDE, in which the nonlinearity enters as a scalar multiple which is non-local. The method of proof does not involve a Lyapounov function. It is shown that stability for the PDE is equivalent to stability for a differential delay equation. Stability for the delay equation is proven by exploiting certain monotonicity properties. These are established by using the methods of optimal control theory.

Global Stability for a Class of Nonlinear PDE with Non-local Term