An application of L-p - L-q decay estimates to the semi-linear wave equation with parabolic-like structural damping

作者：D'Abbicco M; Ebert M R^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2014, 99: 16-34.

DOI：10.1016/j.na.2013.12.021

• Semi-linear wave models
• Fractional damping
• Semi-linear parabolic equations
• Critical exponent
• Global existence

In this paper we study the global existence of small data solutions to u(tt) - Delta u + 2a(-Delta)(sigma) u(t) = |u|(p), u(0, x) = u(0)(x), u(t)(0, x) = u(1)(x), where a > 0, sigma is an element of (0, 1/2] and p > 1. Assuming small data in some Sobolev spaces, we obtain the global existence for p > 1 + 2/(n - 2 sigma), in space dimension n <= (n) over bar, where (n) over bar = (n) over bar(sigma) NE arrow infinity as sigma -> 1/2. In particular, our result holds in any space dimension n >= 2 if sigma = 1/2.

• 出版日期2014-4