In this work,we are concerned with the Timoshenko-Fourier system in both equal and non-equal wave speeds,which admits a non-symmetric dissipation.Furthermore,the dissipative mechanism of regularity-loss type will occu...In this work,we are concerned with the Timoshenko-Fourier system in both equal and non-equal wave speeds,which admits a non-symmetric dissipation.Furthermore,the dissipative mechanism of regularity-loss type will occur in the case of non-equal wave speeds.We establish the global-in-time existence of solutions to the Timoshenko-Fourier system in critical Besov spaces with the regularity s=3/2.展开更多
This paper investigates the decay properties of solutions to the Cauchy problem for viscoelastic nonlinear hyperbolic dissipative systems on R^(3).Due to the weak dissipation of the system,the decay estimate of soluti...This paper investigates the decay properties of solutions to the Cauchy problem for viscoelastic nonlinear hyperbolic dissipative systems on R^(3).Due to the weak dissipation of the system,the decay estimate of solutions exhibits a loss of regularity,implying that a higher regularity of initial data is required for optimal decay rates compared to the global existence.The aim is to reduce the initial regularity to the lowest possible level to achieve the optimal decay rate.Based on the global existence,we employ energy methods,L^(p)-L^(q)-L^(r) estimates,and harmonic analysis tools to obtain the optimal decay result of solutions.展开更多
基金supported by the National Natural Science Foundation of China(No.12001269)the Fundamental Research Funds for the Central Universities of China.
文摘In this work,we are concerned with the Timoshenko-Fourier system in both equal and non-equal wave speeds,which admits a non-symmetric dissipation.Furthermore,the dissipative mechanism of regularity-loss type will occur in the case of non-equal wave speeds.We establish the global-in-time existence of solutions to the Timoshenko-Fourier system in critical Besov spaces with the regularity s=3/2.
文摘This paper investigates the decay properties of solutions to the Cauchy problem for viscoelastic nonlinear hyperbolic dissipative systems on R^(3).Due to the weak dissipation of the system,the decay estimate of solutions exhibits a loss of regularity,implying that a higher regularity of initial data is required for optimal decay rates compared to the global existence.The aim is to reduce the initial regularity to the lowest possible level to achieve the optimal decay rate.Based on the global existence,we employ energy methods,L^(p)-L^(q)-L^(r) estimates,and harmonic analysis tools to obtain the optimal decay result of solutions.
