Hyperbolic–parabolic singular perturbation for quasilinear equations of Kirchhoff type
نویسندگان
چکیده
منابع مشابه
A quasilinear parabolic singular perturbation problem
in a pointwise sense and in a viscosity sense. Here uν denotes the derivative of u with respect to the inward unit spatial normal ν to the free boundary ∂{u > 0}, M = ∫ β(s) ds, α(ν,M) := Φ−1 ν (M) andΦν(α) := −A(αν)+αν ·F(αν), where A(p) is such that F(p) = ∇A(p) with A(0) = 0. Some of the results obtained are new even when the operator under consideration is linear. 2000 Mathematics Subject C...
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Consider the singular perturbation problem for εu(t; ε) + u(t; ε) = Au(t; ε) + ∫ t 0 K(t− s)Au(s; ε) ds+ f(t; ε) , where t ≥ 0, u(0; ε) = u0(ε), u (0; ε) = u1(ε), and w(t) = Aw(t) + ∫ t 0 K(t− s)Aw(s)ds+ f(t) , t ≥ 0 , w(0) = w0 , in a Banach space X when ε → 0. Here A is the generator of a strongly continuous cosine family and a strongly continuous semigroup, and K(t) is a bounded linear opera...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2007
ISSN: 0022-0396
DOI: 10.1016/j.jde.2007.02.005