Stability of Equilibrium Solution to a Nonlinear Parabolic Equation under a 3-Point Boundary Condition
نویسندگان
چکیده
Abstract We consider a nonlinear parabolic equation in one space variable, satisfying a three point boundary condition, such as the heat equation when the temperature at the end is controlled by a sensor at the the point η. We show that the integral solution, in the space of continuous functions satisfying the boundary values, converges to the equilibrium solution. This answers a question which had been posed for nonlinear Laplacians such as p-Laplacians, but answered only for the linear case.
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