Gustavo Navarro - Academia.edu (original) (raw)
PhD in Mathematics with emphasis on PDEs, now repurposed to design algorithms and lead people in silicon valley.
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Papers by Gustavo Navarro
SIAM Journal on Mathematical Analysis, 2017
The two-phase Stefan problem describes the temperature distribution in a homogeneous medium under... more The two-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain, composed of two regions separated by an a priori unknown moving boundary which is transported by the difference (or jump) of the normal derivatives of the temperature in each phase. We establish local-in-time well-posedness and a global-in-time stability result for arbitrary sufficiently smooth domains and small initial temperatures. To this end, we develop a higher-order energy with natural weights adapted to the problem and combine it with Hopf-type inequalities. This extends the previous work by Hadži´Hadži´c & Shkoller [31, 32] on the one-phase Stefan problem to the setting of two-phase problems, and simplifies the proof significantly.
Nonlinearity, 2015
In this paper we study a model of an interface between two fluids in a porous medium. For this mo... more In this paper we study a model of an interface between two fluids in a porous medium. For this model we prove several local and global well-posedness results and study some of its qualitative properties. We also provide numerics.
SIAM Journal on Mathematical Analysis, 2017
The two-phase Stefan problem describes the temperature distribution in a homogeneous medium under... more The two-phase Stefan problem describes the temperature distribution in a homogeneous medium undergoing a phase transition such as ice melting to water. This is accomplished by solving the heat equation on a time-dependent domain, composed of two regions separated by an a priori unknown moving boundary which is transported by the difference (or jump) of the normal derivatives of the temperature in each phase. We establish local-in-time well-posedness and a global-in-time stability result for arbitrary sufficiently smooth domains and small initial temperatures. To this end, we develop a higher-order energy with natural weights adapted to the problem and combine it with Hopf-type inequalities. This extends the previous work by Hadži´Hadži´c & Shkoller [31, 32] on the one-phase Stefan problem to the setting of two-phase problems, and simplifies the proof significantly.
Nonlinearity, 2015
In this paper we study a model of an interface between two fluids in a porous medium. For this mo... more In this paper we study a model of an interface between two fluids in a porous medium. For this model we prove several local and global well-posedness results and study some of its qualitative properties. We also provide numerics.