The Stefan problem

By Marcos Antón Amayuelas. 2015

400 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/3b7b71f8a0ea859c0b8d73dd847691bded841402

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Citations in the corpus

Numerical solution of linear and nonlinear partial differential equations using the peridynamic differential operator (2017, background): “Such problems are also known as the Stefan problem which describes the mathematical model where a phase-change occurs as in the case of melting or solidification [9].”
The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (2017, background): “The correct mathematical solution came only via the weak formulation [159] that allows to eliminate the geometry in a first step and concentrate in finding the so-called weak solution.”
Free Boundary Problems for a Lotka–Volterra Competition System (2014, methodology): “For example, it was used to describe the melting of ice in contact with water [21], the modeling of oxygen in the muscle [5], the wound healing [3], the tumor growth [4], and the spreading of species [6, 8, 13, 15].”
On some Free Boundary Problems of the Prey-predator Model (2013, methodology): “For example, it was used to describe the melting of ice in contact with water [28], the modeling of oxygen in the muscle [5], the wound healing [3], the tumor growth [4], and the spreading of species [7, 8, 10, 11, 13, 14, 16, 17, 21, 29, 30].”
Spreading and vanishing in nonlinear diffusion problems with free boundaries (2013, background): “1) coincide with the one-phase Stefan condition arising from the investigation of the melting of ice in contact with water ([22]).”
A diffusive logistic model with a free boundary in time-periodic environment☆ (2013, background): “1) obtained from the above consideration coincides with the one-phase Stefan condition arising from the investigation of the melting of ice in contact with water ([26]).”