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1.
Nasser-eddine Tatar 《Applied Mathematics and Optimization》2012,66(1):123-145
For a prescribed desirable arbitrary decay suitable viscoelastic materials are determined through their relaxation functions. It is shown that if we wish to have a decay of order ??(t) then the kernels should be of the same order. That is their product with this function should be summable. 相似文献
2.
Nasser-eddine Tatar 《Applied Mathematics Letters》2009,22(3):336-340
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. 相似文献
3.
Nasser-eddine Tatar 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(9):3130-3139
In this paper we consider a second-order abstract problem involving derivatives of non-integer order. The existence and uniqueness of mild and classical solutions are established in appropriate spaces under weak assumptions. 相似文献
4.
We consider the Cauchy problem for the fractional differential equation
D1+αu+Dβu=Δu+h(t,x)|u|p