Caloric measure and Reifenberg flatness.
Computation of bifurcated branches in a free boundary problem arising in combustion theory
Computation of bifurcated branches in a free boundary problem arising in combustion theory
We consider a parabolic 2D Free Boundary Problem, with jump conditions at the interface. Its planar travelling-wave solutions are orbitally stable provided the bifurcation parameter does not exceed a critical value . The latter is the limit of a decreasing sequence of bifurcation points. The paper deals with the study of the 2D bifurcated branches from the planar branch, for small k. Our technique is based on the elimination of the unknown front, turning the problem into a fully nonlinear...
Computational studies of anisotropic diffuse interface model of microstructure formation in solidification
Convergence of a lattice numerical method for a boundary-value problem with free boundary and nonlinear Neumann boundary conditions.
Convergence to equilibria for a three-dimensional conserved phase-field system with memory.
Convergent numerical approximations of the thermomechanical phase transitions in shape memory alloys.
Correctors and error estimates in the homogenization of a Mullins–Sekerka problem
Coupled heat transport and Darcian water flow in freezing soils
The model of coupled heat transport and Darcian water flow in unsaturated soils and in conditions of freezing and thawing is analyzed. In this contribution, we present results concerning the existence of the numerical solution. Numerical scheme is based on semi-implicit discretization in time. This work illustrates its performance for a problem of freezing processes in vertical soil columns.
Co-volume methods for degenerate parabolic problems.