Vol. 19, No. 3, 1966

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ISSN: 0030-8730
Asymptotic behavior of solutions of parabolic equations of higher order

Lu-san Chen

Vol. 19 (1966), No. 3, 407–410
Abstract

It is known that the solution u of the heat equation ∂u∕∂t = Δu under the boundary condition u = 0 decays as eλtu for some λ > 0 as t →∞. This gives us information about the asymptotic behavior of the solution u in time.

There arises the question whether such a theorem is valid for parabolic differential equations with variable coefficients.

In this note we shall treat this problem and prove that the theorem analogous to the above holds for parabolic differential inequalities of higher order under some additional restrictions.

Mathematical Subject Classification
Primary: 35.63
Secondary: 35.16
Milestones
Received: 14 June 1965
Published: 1 December 1966
Authors
Lu-san Chen