论文信息 - The non-autonomous wave equation with general Wentzell boundary conditions

The non-autonomous wave equation with general Wentzell boundary conditions

We study the problem of the well-posedness for the abstract Cauchy problem associated to the non-autonomous one-dimensional wave equation utt = A(t)u with general Wentzell boundary conditions Here A(t)u := (a(x, t)ux)x, a(x, t) ≥ ε > 0 in [0, 1] × [0, + ∞) and βj(t) > 0, γj(t) ≥ 0, (γ0(t), γ1(t)) ≠ (0,0). Under suitable regularity conditions on a, βj, γj we prove the well-posedness in a suitable (energy) Hilbert space

[1] Jerome A. Goldstein,et al. Time dependent hyperbolic equations , 1969 .

[2] J. Goldstein,et al. The heat equation with generalized Wentzell boundary condition , 2002 .

[3] H. Fattorini. Second Order Linear Differential Equations in Banach Spaces , 1985 .

[4] J. Goldstein. Semigroups of Linear Operators and Applications , 1985 .

[5] J. Goldstein. Semigroups and second-order differential equations , 1969 .

[6] Jerome A. Goldstein,et al. Oscillatory boundary conditions for acoustic wave equations , 2003 .

[7] Tosio Kato,et al. Integration of the equation of evolution in a Banach space , 1953 .

[8] Tosio Kato,et al. On linear differential equations in banach spaces , 1956 .