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On Existence and Uniqueness of Solutions for Semilinear Fractional Wave Equations

Volume: 20, Issue: 1, Pages: 117 - 138
Published: Feb 1, 2017
Abstract
Let Ω be a 𝒞2-bounded domain of ℝd, d = 2,3, and fix Q = (0,T)× Ω with T ∈ (0,+∞]. In the present paper we consider a Dirichlet initial-boundary value problem associated to the semilinear fractional wave equation ∂tαu+Au=fb(u)inQwhere1<α<2,∂tα corresponds to the Caputo fractional derivative of order α, 𝒜 is an elliptic operator and the nonlinearity fb ∈ 𝒞1 (ℝ) satisfies fb(0) = 0 and |fb′(u)|⩽C|u|b−1 for some b > 1. We first provide a...
Paper Details
Title
On Existence and Uniqueness of Solutions for Semilinear Fractional Wave Equations
Published Date
Feb 1, 2017
Volume
20
Issue
1
Pages
117 - 138
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