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- W2027757210 abstract "We study the Cauchy problem for non-linear dissipative evolution equations formula math. where L is the linear pseudodifferential operator Lu=F ξ→x (L(ξ)u(ξ)) and the non-linearity is a quadratic pseudodifferential operator N(u) = F ξ→x ∫ R a(t,ξ,y)u(t,ξ-y)u(t,y)dy u≡F x→ξ u is the Fourier transformation. We consider non-convective type non-linearity, that is we suppose that a(t,0,y)¬=0. Let the initial data u 0 ∈H? ,0 ∩H 0,e ,?>1 2, are sufficiently small and have a non-zero total mass ∫u 0 (x) dx¬=0, where H n,m = {Φ∈L 2 ∥ m n Φ(x)∥ L 2<∞} is the weighted Sobolev space. Then we give the main term of the large time asymptotics of solutions in the sub critical case." @default.
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- W2027757210 date "2005-01-01" @default.
- W2027757210 modified "2023-10-16" @default.
- W2027757210 title "Asymptotics of solutions for sub critical non-convective type equations" @default.
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- W2027757210 doi "https://doi.org/10.1002/mma.558" @default.
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