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EXISTENCE OF GLOBAL WEAK SOLUTIONS FOR A p-LAPLACIAN INEQUALITY WITH STRONG DISSIPATION IN NONCYLINDRICAL DOMAINS
(Texas State Univ, 2022) Ferreira, Jorge; Piskin, Erhan; Shahrouzi, Mohammad; Cordeiro, Sebastiao; Raposo, Carlos Alberto
In this work, we obtain global solutions for nonlinear inequalities of p -Laplacian type in noncylindrical domains, for the unilateral problem with strong dissipation u '' - delta(pu) - delta u ' -f >= 0 in Q(0), where delta(p) is the nonlinear p -Laplacian operator with 2 <= p < infinity, and Q(0) is the noncylindrical domain. Our proof is based on a penalty argument by J. L. Lions and Faedo-Galerkin approximations.
Rao–Nakra sandwich beam with second sound
(Elsevier B.V., 2021) Raposo, Carlos Alberto; Ferreira, Jorge; Pişkin, Erhan; Villagrán, Octavio Paulo Vera
In this manuscript, we prove the well-posedness and exponential stability for a thermoelastic structure given by a Rao–Nakra sandwich beam. The system consists of two wave equations for the longitudinal displacements of the top and bottom layers, and one Euler–Bernoulli beam equation for the transversal displacement, where, the thermal disturbances are modeled by the propagation of wave-like pulses traveling at a finite speed, that is, we remove the physical paradox of infinite propagation speed in the classical theory of thermoelasticity within Fourier's law by using Cattaneo's law for heat conduction.