Global existence for damped σ-evolution equations with nonlocal nonlinearity

2021/07/29 by Said, Khaldi
#35B45 #35G10 #42B10 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.13924

Abstract

In this research, we would like to study the global (in time) existence of small data solutions to the following damped σ-evolution equations with nonlocal (in space) nonlinearity: ∂_t²u+(-Δ)^σu+∂_tu+(-Δ)^σ∂_tu=I_α(|u|^p), tgt;0, x∈ ℝⁿ, where σ≥1, p>1 and I_α is the Riesz potential of power nonlinearity |u|^p for any α∈ (0,n). More precisely, by using the (L^m∩ L²)-L² and L²-L² linear estimates, where m∈[1,2], we show the new influence of the parameter α on the admissible ranges of the exponent p.

Related

• A remark on semi-linear damped σ-evolution equations with a modulus of continuity term in nonlinearity
• Effect of different additional L^m regularity on semi-linear damped σ-evolution models
• Global existence for weakly coupled systems of semi-linear structurally damped σ-evolution models with different power nonlinearities
• Decay characterization of solutions to semi-linear structurally damped σ-evolution equations with time-dependent damping
• Effect of additional regularity for the initial data on semi-linear σ-evolution equations with different damping types