Abstract: This paper is devoted to proving L -estimates for the solution of semilinear parabolic equations. The uniform estimates are obtained on the infinite time interval under the assumption that the solution is square inte grable. This setting is useful for stabilization problems formulated as optimal control problems. The inhomogenous forcing function are chosen as elements of anisotropic Lebesgue spaces. Different boundary conditions on bounded domains with a Lipschitz continuous boundary are investigated.

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