In this paper we study a class of parabolic initial boundary value problems relative to an operator whose the prototype is u_t−Ze^W(x)div(∇uZ^(−1)e ^(−W(x))) = g, where W(x) is a smooth function and Z is a constant. We obtain an estimate of the solution comparing it with the solution to a problem relative to the operator u_t− 1/ϕ(x) (u_(x_1)ϕ(x))_(x_1)=G, where ϕ(x) is the density of Gauss measure, G is a function related to g and the data depend only on the time variable and the first space variable.
Parabolic equation related to Boltzmann measure
FEO, Filomena
2009-01-01
Abstract
In this paper we study a class of parabolic initial boundary value problems relative to an operator whose the prototype is u_t−Ze^W(x)div(∇uZ^(−1)e ^(−W(x))) = g, where W(x) is a smooth function and Z is a constant. We obtain an estimate of the solution comparing it with the solution to a problem relative to the operator u_t− 1/ϕ(x) (u_(x_1)ϕ(x))_(x_1)=G, where ϕ(x) is the density of Gauss measure, G is a function related to g and the data depend only on the time variable and the first space variable.File in questo prodotto:
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