ISSN:
1432-0673
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract We prove short-time well-posedness of the Cauchy problem for incompressible strongly elliptic hyperelastic materials. Our method consists in: a) Reformulating the classical equations in order to solve for the pressure gradient (The pressure is the Lagrange multiplier corresponding to the constraint of incompressibility.) This formulation uses both spatial and material variables. b) Solving the reformulated equations by using techniques which are common for symmetric hyperbolic systems. These are: 1) Using energy estimates to bound the growth of various Sobolev norms of solutions. 2) Finding the solution as the limit of a sequence of solutions of linearized problems. Our equations differ from hyperbolic systems, however, in that the pressure gradient is a spatially non-local function of the position and velocity variables.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00278241
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