Abstract
<abstract><p>In this paper, a swelling soil system with two nonlinear dampings of variable exponent-type is considered. The stability analysis of this system is investigated and it is proved that the system is stable under a natural condition on the parameters of the system and the variable exponents. It is noticed that one variable damping is enough to achieve polynomial and exponential decay and the decay is not necessarily improved if the system has two variable dampings.</p></abstract>
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