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Stability in fully nonlinear parabolic equations

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We study the stability of the null solution of a class of nonlinear evolution equations in Banach space. After stating a local existence result and the principle of linearized stability, we study the critical case, giving sufficient conditions for stability. The results are applied to second-order fully nonlinear parabolic equations in [0, + ∞ [ × R n.

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Communicated by C. Dafermos

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Lunardi, A. Stability in fully nonlinear parabolic equations. Arch. Rational Mech. Anal. 130, 1–24 (1995). https://doi.org/10.1007/BF00375654

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