Geodesic
Stabilization of Solution to the Cauchy Problem for a Parabolic Equation with Lower Order Coefficients and an Exponentially Growing Initial Function
Informatics and Automation, Differential equations and dynamical systems, Tome 261 (2008), pp. 97-100 
V. N. Denisov. Stabilization of Solution to the Cauchy Problem for a Parabolic Equation with Lower Order Coefficients and an Exponentially Growing Initial Function. Informatics and Automation, Differential equations and dynamical systems, Tome 261 (2008), pp. 97-100. http://geodesic.mathdoc.fr/item/TRSPY_2008_261_a7/
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     title = {Stabilization of {Solution} to the {Cauchy} {Problem} for {a~Parabolic} {Equation} with {Lower} {Order} {Coefficients} and an {Exponentially} {Growing} {Initial} {Function}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

For the coefficients of lower order terms of a second-order parabolic equation, we obtain sharp sufficient conditions under which the solution of the Cauchy problem stabilizes to zero uniformly in $x$ on each compact set $K$ in $\mathbb R^N$ for any exponentially growing initial function.

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