Analyticity and regularity for a class of second order evolution equations

Alain Haraux, Mitsuharu Otani

    研究成果: Article査読

    8 被引用数 (Scopus)


    The regularity conservation as well as the smoothing effect are studied for the equation u″+Au+cAαu′ = 0, where A is a positive selfadjoint operator on a real Hilbert space H and α ∈ (0, 1]; c > 0. When α ≥ 1/2 the equation generates an analytic semigroup on D(A1/2) × H, and if α ∈ (0, 1/2) a weaker optimal smoothing property is established. Some conservation prop- erties in other norms are also established, as a typical example, the strongly dissipative wave equation utt – Δu – cΔut = 0 with Dirichlet boundary conditions in a bounded domain is given, for which the space C0(Ω) × C0(Ω) is conserved for t > 0, which presents a sharp contrast with the conservative case utt – Δu = 0 for which C0()-regularity can be lost even starting from an initial state (u0, 0) with u0 2 C0(Ω) ⋂ C1(Ω).

    ジャーナルEvolution Equations and Control Theory
    出版ステータスPublished - 2013

    ASJC Scopus subject areas

    • 応用数学
    • 制御と最適化
    • モデリングとシミュレーション


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