Work

Decay character and the semilinear structurally damped σ-evolution equations with two dissipative terms

Year: 2024

Type: article

Abstract: In this paper, we study the decay rates of the solution and its derivatives to the Cauchy problem for the linear damped σ -evolution equation with two dissipative dampings u t t + ( − Δ ) σ u + ( − Δ ) δ 1 u t + ( − Δ ) δ 2 u t = 0 that are expressed in terms of decay characters of the initial data. Furthermore, by using the decay rates of solutions to the linear part and the fixed-point method, we investigate the existence and decay rate of the global solution with small data of the corresponding semi-linear problems with the nonlinear term of power type | u t | p , for the supercritical case p > p ⁎ . For some special data spaces, the optimality of p ⁎ is guaranteed by nonexistence results in the subcritical case p < p ⁎ and the critical case p = p ⁎ .

Source: Journal of Mathematical Analysis and Applications

DOI: 10.1016/j.jmaa.2024.129100

Authors: Cung The Anh, Pham Trieu Duong, Tang Trung Loc

Institution: Hanoi National University of Education

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,100

Funders: Trường Đại học Sư phạm Hà Nội, National Foundation for Science and Technology Development