Work

On the Cauchy problem for semilinear thermoelastic plate systems in the Lq framework

Year: 2025

Type: article

Abstract: We mainly consider semilinear thermoelastic plate systems with general power nonlinearities in the whole space $ \mathbb{R}^n $. By applying the Fourier analysis, some sharp $ (L^q\cap L^m)-L^q $ estimates of solutions (with any $ 1\leqslant m\leqslant q\leqslant +\infty $) to the classical thermoelastic plate system are derived, which cover all known results in $ \mathbb{R}^n $. Then, we investigate global in time existence of small data $ L^q $ solutions (with any $ q\in[1,+\infty] $) and blow-up of weak solutions for the semilinear thermoelastic plate systems under suitable conditions on the power exponents, which justify critical exponents for several classes of nonlinearities.

Source: Evolution equations and control theory

DOI: 10.3934/eect.2025044

Authors: Halit Sevki Aslan, Wenhui Chen

Institutions: Universidade de São Paulo, Guangzhou University

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

Funders: Fundação de Amparo à Pesquisa do Estado de São Paulo, National Natural Science Foundation of China, Technische Universität Bergakademie Freiberg, Basic and Applied Basic Research Foundation of Guangdong Province