Quasi-linear Parabolic Systems in Divergence Form with Weak Monotonicity
نویسنده
چکیده
We consider the initial and boundary value problem for the quasi-linear parabolic system ∂u ∂t − div σ (x, t, u(x, t),Du(x, t)) = f on × (0, T ), u(x, t) = 0 on ∂ × (0, T ), u(x, 0) = u0(x) on for a function u : × [0, T ) → R with T > 0. Here, f ∈ Lp(0, T ;W−1,p ( ;Rm)) for some p ∈ (2n/(n + 2),∞), and u0 ∈ L2( ;Rm). We prove existence of a weak solution under classical regularity, growth, and coercivity conditions for σ but with only very mild monotonicity assumptions.
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تاریخ انتشار 2001