1,721,251 research outputs found
Some remarks on a problem of percolation in gently sloping beaches
No full textWe study a free boundary problem related to a model of unsteady flow of a fluid through a special porous medium, precisely a gently sloping beach, when an asymptotic formulation is considered (see a paper by J. M. Aitchison, C. M. Elliott and J. R. Ockendon [I.M.A. J. Appl. Math. 30 (1983), no. 3, 269–287; MR0719980] for details). We achieve a variational formulation of the problem for which we show existence and uniqueness of the solution
Global existence for a second-order thermo-mechanical model of shape memory alloys
No full textAbstractA thermo-mechanical model of structural phase transitions in solids is considered. In this model the free energy depends on temperature, macroscopic deformation, and also on the proportions of the phases. The related initial-boundary value problem consists of equilibrium equations for energy and momentum coupled with an evolution variational inequality for the phase proportions. Fourth-order regularizing terms are neglected in the momentum balance equation. Using an approximation—a priori estimates—passage to the limit procedure we show the existence of a solution in any dimension of space
Mathematical study of an evolution problem describing the thermomechanical process in shape memory alloys
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