On the decay of a solution of a nonuniformly parabolic equation
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For a uniformly parabolic second-order equation with lower-order terms in an unbounded domain, we obtain an upper bound for the decay rate of the solution of the mixed problem with alternating boundary conditions of the first and third types. We prove that the bound is sharp in the case of an equation without lower-order terms in a wide class of domains of revolution. In addition, we show that a solution of a nonuniformly parabolic equation can decay much more rapidly than a solution of a uniformly parabolic equation.
KeywordsDecay Rate Parabolic Equation Unbounded Domain Mixed Problem Harnack Inequality
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- 10.Mukminov, F.Kh., Stabilization of Solutions of the First Mixed Problem for the System of Navier-Stokes Equations, Doctoral (Phys.-Math.) Dissertation, Moscow, 1994.Google Scholar