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排序方式: 共有160条查询结果,搜索用时 281 毫秒
1.
Piotr Rybka 《Journal of Differential Equations》2002,181(2):340-366
We study the behavior of solutions of the modified Stefan problem in the plane for polygonal interfaces. We are particularly interested in a solution near a singularity of either the loss of a facet or the breaking of a facet. We establish precise regularity results if a facet disappears. We use them to establish the existence of a weak solution with singular data, i.e., when some of the zero-crystalline-curvature facets have zero length. 相似文献
2.
ADegenerateStefanProblemwithTwoFreeBoundaries¥(李辉来)LiHuilai(DepartmentofMathematics,JilinUniversity,Changchun,130023)Abstract... 相似文献
3.
Vincenzo Recupero 《Journal of Mathematical Analysis and Applications》2004,300(2):387-407
In this paper we study a model of phase relaxation for the Stefan problem with the Cattaneo–Maxwell heat flux law. We prove an existence and uniqueness result for the resulting problem and we show that its solution converges to the solution of the Stefan problem as the two relaxation parameters go to zero, provided a relation between these parameters holds. 相似文献
4.
In this article, an ALE finite element method to simulate the partial melting of a workpiece of metal is presented. The model includes the heat transport in both the solid and liquid part, fluid flow in the liquid phase by the Navier–Stokes equations, tracking of the melt interface solid/liquid by the Stefan condition, treatment of the capillary boundary accounting for surface tension effects and a radiative boundary condition. We show that an accurate treatment of the moving boundaries is crucial to resolve their respective influences on the flow field and thus on the overall energy transport correctly. This is achieved by a mesh‐moving method, which explicitly tracks the phase boundary and makes it possible to use a sharp interface model without singularities in the boundary conditions at the triple junction. A numerical example describing the welding of a thin‐steel wire end by a laser, where all aforementioned effects have to be taken into account, proves the effectiveness of the approach.Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
5.
S.L. Mitchell 《Applied Mathematical Modelling》2012,36(1):127-138
In this paper the combined integral method is applied to a simple one-dimensional ablation problem. One of the drawbacks of heat balance integral methods is how to choose the approximating function. It is common to use a polynomial form but even then it is not clear what the power of the highest order term should be. Previous studies have determined exponents either from exact solutions or from expansions valid over short time scales; neither approach is satisfactory nor very accurate for larger times. We combine the heat balance and refined integral methods to determine this exponent as part of the solution process, and conclude that it is in fact time-dependent in the ablation stage. From comparing the approximate solutions with numerical and exact analytical solutions whenever possible, we show that this new method greatly improves the accuracy on standard methods, without overcomplicating the method. 相似文献
6.
Roberto Gianni Paola Mannucci 《NoDEA : Nonlinear Differential Equations and Applications》2001,8(2):219-235
We prove a well posedness result for a free boundary problem describing the filtration of an incompressible viscous fluid
in a porous medium containing water absorbing granules.?The location of the wetting front (the free boundary) is described
by a Stefan like problem for a parabolic equation which is coupled with an hyperbolic equation describing the absorption kinetic
of the granules.
Received December 1999 相似文献
7.
Two explicit error representation formulas are derived for degenerate parabolic PDEs, which are based on evaluating a parabolic residual in negative norms. The resulting upper bounds are valid for any numerical method, and rely on regularity properties of solutions of a dual parabolic problem in nondivergence form with vanishing diffusion coefficient. They are applied to a practical space-time discretization consisting of piecewise linear finite elements over highly graded unstructured meshes, and backward finite differences with varying time-steps. Two rigorous a posteriori error estimates are derived for this scheme, and used in designing an efficient adaptive algorithm, which equidistributes space and time discretization errors via refinement/coarsening. A simulation finally compares the behavior of the rigorous a posteriori error estimators with a heuristic approach, and hints at the potentials and reliability of the proposed method.
8.
Przemys?aw Górka 《Journal of Mathematical Analysis and Applications》2008,341(2):1413-1426
We examine the evolution of crystals in three dimensions. We assume that the Wulff shape is a prism with a hexagonal base. We include the Gibbs-Thomson law on the crystal surface and the so-called Stefan condition. We show local in time existence of solutions assuming that the initial crystal has admissible shape. 相似文献
9.
MCGUINNESS M. J.; PLEASE C. P.; FOWKES N.; MCGOWAN P.; RYDER L.; FORTE D. 《IMA Journal of Management Mathematics》2000,11(1):49-70
Three models are presented for the wetting of whole grains ofcereal. Two are for temperatures below gelatinization temperatures,one of which incorporates the effects of swelling of the grain.A third model is presented for wetting of a grain at temperaturesabove gelatinization, and hence cooking the grain. The modelsare developed as partial differential equations, and solvedin a variety of ways. A model that ignores swelling at temperaturesbelow gelatinization is solved for wetting times by using theconcept of mean action time, which reduces the problem to anexactly solvable linear Poisson equation. The other two models,which include swelling and cooking respectively, are solvedapproximately, taking advantage of the steep nonlinear diffusionfronts that develop. The aim of the modelling is to improveunderstanding of the cooking of whole-grain cereals prior toprocessing into breakfast cereals. Moisture penetration curvesare obtained and compared. Regions where the penetration rateis approximately linear are noted, suggesting that nonlineardiffusion equations are a promising way to model grain wettingand cooking. 相似文献
10.
We consider a steady-state heat conduction problem P
α
with mixed boundary conditions for the Poisson equation depending on a positive parameter α , which represents the heat transfer coefficient on a portion Γ
1
of the boundary of a given bounded domain in R
n
. We formulate distributed optimal control problems over the internal energy g for each α . We prove that the optimal control g_ op
α
and its corresponding system u_ g_ op
α
α and adjoint p_ g_ op
α
α states for each α are strongly convergent to g
op
, u_ g
op
and p _ g
op
, respectively, in adequate functional spaces. We also prove that these limit functions are respectively the optimal control,
and the system and adjoint states corresponding to another distributed optimal control problem for the same Poisson equation
with a different boundary condition on the portion Γ
1
. We use the fixed point and elliptic variational inequality theories. 相似文献