Some Remarks on the Asymptotic Profile of Solutions to Structurally Damped σ‐Evolution Equations
Abstract
ABSTRACT In this paper, we are interested in analyzing the asymptotic profiles of solutions to the Cauchy problem for structurally damped ‐evolution equations in ‐sense. Depending on the parameters and we would like to not only indicate the approximation formula of solutions to both linear and nonlinear problems but also recognize the optimality of their decay rates in the distinct cases of parabolic like damping and ‐evolution like damping when the spatial dimension is sufficiently high. Moreover, some sharp blow‐up solution results for the low dimensional cases of the corresponding linear equation are also discussed in this work.
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Nonlinear Differential Equations Analysis
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Mathematical Methods in the Applied Sciences
- Publisher
- Wiley
- Volume
- 49
- Issue
- 13
- Pages
- 15327–15357
- Publication date
- 2 June 2026
- Language
- EN