756 research outputs found
Long-Time Behavior of Quasilinear Thermoelastic Kirchhoff-Love Plates with Second Sound
We consider an initial-boundary-value problem for a thermoelastic Kirchhoff &
Love plate, thermally insulated and simply supported on the boundary,
incorporating rotational inertia and a quasilinear hypoelastic response, while
the heat effects are modeled using the hyperbolic Maxwell-Cattaneo-Vernotte law
giving rise to a 'second sound' effect. We study the local well-posedness of
the resulting quasilinear mixed-order hyperbolic system in a suitable solution
class of smooth functions mapping into Sobolev -spaces. Exploiting the
sole source of energy dissipation entering the system through the hyperbolic
heat flux moment, provided the initial data are small in a lower topology
(basic energy level corresponding to weak solutions), we prove a nonlinear
stabilizability estimate furnishing global existence & uniqueness and
exponential decay of classical solutions.Comment: 46 page
Higher order evolution inequalities involving Leray-Hardy potential singular on the boundary
We consider a higher order (in time) evolution inequality posed in the half ball, under Dirichlet type boundary conditions. The involved elliptic operator is the sum of a Laplace differential operator and a Leray-Hardy potential with a singularity located at the boundary. Using a unified approach, we establish a sharp nonexistence result for the evolution inequalities and hence for the corresponding elliptic inequalities. We also investigate the influence of a nonlinear memory term on the existence of solutions to the Dirichlet problem, without imposing any restrictions on the sign of solutions
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