ON THE STABILITY OF SEMILINEAR NONAUTONOMOUS EVOLUTION EQUATIONS IN BANACH SPACES AND ITS APPLICATION TO STRONGLY PARABOLIC EQUATIONS


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Abstract

The paper is concerned with the exponential stability of the zero solution of strongly nonautonomous parabolic equations. Conditions are found on time-dependent coefficients of a parabolic equation under which its solutions converge exponentially to 0 as t → ∞.

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