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This paper is concerned with the dynamics of nonlinear one-dimensional beam equations. We consider nonlinear beam equations with viscosity or with a lower-order damping term instead of the viscosity, and we establish the existence of global attractors for both systems.
We characterize the basal mass balance of the Ekström Ice Shelf, Dronning Maud Land, Antarctica, using interferometrically derived surface velocities and ice thickness measurements from radio-echo sounding (RES). The surface velocities are based on data from European Remote-sensing Satellites-1 and -2 (ERS-1/2) during 1994–97. The ice thickness grid consists of 136 RES profiles acquired between 1996 and 2006. Mass fluxes are calculated along selected RES profiles where possible, to reduce uncertainties from ice thickness interpolation. Elsewhere large-scale mass fluxes are calculated using interpolated ice thickness data. Themass flux into the Ekström Ice Shelf from the main grounded drainage basins is estimated to be 3.19±0.4Gt a–1. The mass flux near the ice shelf front is 2.67±0.3Gt a–1. Assuming steady state, and based on the equation of continuity, we interpret the residual mass flux as a combined effect of snow accumulation and subglacial melting/refreezing. Using net snow accumulation rates from previous studies, we link the mass flux divergence in irregular-shaped polygons to processes beneath the ice shelf. The highest subglacial melt rates of ~1.1ma–1 are found near the grounding zone of two main inflow glaciers, and around the German station Neumayer III. The detection of unlikely refreezing in a small area ~15 km west of Neumayer III is attributed to both dataset inaccuracies and a (possibly past) violation of the steady-state assumption. In general, the method and input data allow mapping of the spatial distribution of basal melting and the results are in good agreement with several previous studies.
We consider initial boundary value problems for the equations of linear thermoelasticity in both bounded and unbounded domains and for both nonhomogeneous and anisotropic media. For bounded domains, it is shown that the unique solution of the problem is time-asymptotically equal to the solution of a particular initial boundary value problem which is obtained from a natural decomposition of the original initial data and which represents a (in general non-vanishing) time harmonic part. For the unbounded case similar results are obtained, but now in the sense of weak convergence which lead to the result of local energy decay: the solution tends to zero in every compactum.
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