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How far can relaxation functions be increasing in viscoelastic problems? (English) Zbl 1154.74327

Summary: It is known that when we add a viscoelastic damping to a frictional damping acting in the domain we might lose the property of exponential stability of the system. Moreover, a necessary condition for a system to be sub-exponentially stable is that the kernel itself must be sub-exponentially decaying to zero. Having this in mind, a natural question to be asked is that of when this necessary condition is also sufficient. We prove that this is the case for a fairly large class of kernels.

MSC:

74D10 Nonlinear constitutive equations for materials with memory
74M10 Friction in solid mechanics
74D05 Linear constitutive equations for materials with memory
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