AbstractIn this paper, we study a plate equation as a model for a suspension bridge with time-varying delay and time-varying weights. Under some conditions on the delay and weight functions, we establish a stability result for the associated energy functional. The present work extends and generalizes some similar results in the case of wave or plate equations.
This paper deals with the global uniqueness of an inverse problem for
the stochastic plate with structural damping. The key point is the
Carleman estimate for the fourth order stochastic plate operators dyt −
ρ∆ytdt + ∆2ydt. To this aim, a weighted point- wise identity for a
fourth order stochastic plate operator is established, via which we
obtained the desired Carleman estimate for the corresponding stochastic
plate equation with structural damping.
In this paper, we consider the Cauchy problem for a family of
evolution-parabolic coupled systems, which are related to the classical
thermoelastic plate equations containing non-local operators. By using
diagonalization procedure and WKB analysis, we derive representation of
solutions in the phase space. Then, sharp decay properties in a
framework of $L^p-L^q$ are investigated via these
representations. Particularly, some thresholds for the regularity-loss
type decay properties are found.
<abstract><p>In this paper, we consider the Cauchy problem for a family of evolution-parabolic coupled systems, which are related to the classical thermoelastic plate equations containing non-local operators. By using diagonalization procedure and WKB analysis, we derive representation of solutions in the phase space. Then, sharp decay properties in a framework of $ L^p-L^q $ are investigated via these representations. Particularly, some thresholds for the regularity-loss type decay properties are found.</p></abstract>
<p style='text-indent:20px;'>This paper studies a coupled system of plate equations with variable coefficients, subject to the clamped boundary conditions. By the Riemannian geometry approach, the duality method, the multiplier technique and a compact perturbation method, we establish exact boundary null controllability of the system under verifiable assumptions.</p>
On the existence theory for nonlinear plate equations
