We consider the initial value problem for a possibly degenerate in-tegrodifferential equation in L2(Ω) (eqution found) where M(t) = M0M1(t) is the multiplication operator by the function m(x, t) = m0(x)m1(x, t), m0(x) ≥ 0, m1(x, t) ≥ c > 0, L(t) is the realization in L2(Ω) of a second-order strongly elliptic operator in divergence form with Dirichlet or Neumann boundary conditions for all t, and B(t, s) is a linear differential operator of order ≤ 2 for each (t, s), 0 ≤ s ≤ t ≤ T, Ω being a bounded open set in Rn with a smooth boundary. We also establish a corresponding result in Lp(Ω), 1 < p < 3/2, related to Dirichlet boundary condition, only.
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Degenerate integrodifferential equations of parabolic type / A. Favini, A. Lorenzi, H. Tanabe - In: Differential equations : inverse and direct problems / [a cura di] A. Favini, A. Lorenzi. - [s.l] : Chapman & Hall/CRC, 2006. - ISBN 1584886048. - pp. 91-109
Degenerate integrodifferential equations of parabolic type
A. LorenziSecondo
;
2006
Abstract
We consider the initial value problem for a possibly degenerate in-tegrodifferential equation in L2(Ω) (eqution found) where M(t) = M0M1(t) is the multiplication operator by the function m(x, t) = m0(x)m1(x, t), m0(x) ≥ 0, m1(x, t) ≥ c > 0, L(t) is the realization in L2(Ω) of a second-order strongly elliptic operator in divergence form with Dirichlet or Neumann boundary conditions for all t, and B(t, s) is a linear differential operator of order ≤ 2 for each (t, s), 0 ≤ s ≤ t ≤ T, Ω being a bounded open set in Rn with a smooth boundary. We also establish a corresponding result in Lp(Ω), 1 < p < 3/2, related to Dirichlet boundary condition, only.Pubblicazioni consigliate
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