Parabolic problems for the Anderson model |
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Authors: | J Gärtner S A Molchanov |
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Institution: | Technische Universit?t, FB Mathematik, Strasse des 17. Juni 136, D-10623 Berlin, Germany e-mail: jg@math.tu-berlin.de, DE Department of Mathematics, University of North Carolina, Charlotte, NC 28223-9998, USA, US
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Abstract: | Summary. This is a continuation of our previous work 6] on the investigation of intermittency for the parabolic equation (∂/∂t)u=Hu on ℝ+×ℤ
d
associated with the Anderson Hamiltonian H=κΔ+ξ(·) for i.i.d. random potentials ξ(·). For the Cauchy problem with nonnegative
homogeneous initial condition we study the second order asymptotics of the statistical moments <u(t,0)
p
> and the almost sure growth of u(t,0) as t→∞. We point out the crucial role of double exponential tails of ξ(0) for the formation of high intermittent peaks of the
solution u(t,·) with asymptotically finite size. The challenging motivation is to achieve a better understanding of the geometric structure
of such high exceedances which in one or another sense provide the essential contribution to the solution.
Received: 10 December 1996 / In revised form: 30 September 1997 |
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Keywords: | Mathematics Subject Classification (1991): Primary 60H25 82C44 Secondary 60F10 60K40 |
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