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On Stabilization of the Solution of the Cauchy Problem for a Parabolic Equation with a Lower Order Coefficient and a Growing Initial Function

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Abstract

The paper deals with the study of sufficient conditions on the coefficients of a second-order partial differential equation, ensuring the stabilization to zero of the solution of the Cauchy problem uniformly in x on any compact set K ⊂ ℝN for any continuous initial function u 0(x), growing at infinity not faster than some power of |x|m, m > 0.

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  1. V. N. Denisov
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Denisov, V.N. On Stabilization of the Solution of the Cauchy Problem for a Parabolic Equation with a Lower Order Coefficient and a Growing Initial Function. Journal of Mathematical Sciences 120, 1313–1327 (2004). https://doi.org/10.1023/B:JOTH.0000016051.61775.e7

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  • DOI: https://doi.org/10.1023/B:JOTH.0000016051.61775.e7

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