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BCAMSevero Ochoa Award

basque center for applied mathematics

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Stan, Diana

Postdoc Fellow - (Juan de la Cierva 2015)

Linear and Non-Linear Waves

Mazarredo, 14. 48009 Bilbao Basque Country - Spain


Since January 2016, I am Postdoctoral Researcher at the Basque Center of Applied Mathematics in the research area of Fluid Mechanics (Mathematical Physics), in the group of Professor Luis Vega. Our main research interests in the collaboration with BCAM are: fractional diffusion operators and their probabilistic motivation (Levy processes and anomalous diffusion), fractional partial differential equations of diffusion/dispersive type.

Main collaborators at BCAM: Luis Vega (on positivity estimates for fractional diffusion equations), Gianni Pagnini (fractional diffusion), Felix del Teso (fractional diffusion).

My main field of research is nonlinear partial differential equations. So far, I have been working on the following directions:
• Local Nonlinear Diffusion Equations (Porous Medium Equation, Doubly Nonlinear Diffusion Equation),
• Nonlocal Nonlinear Diffusion Equations both in divergence and nondivergence form (Fractional Porous Medium Equations, Fisher-KPP equation with nonlinear fractional diffusion),
• Dispersive Equations (Schrodinger Equation).
My research is focused on the qualitative properties of the above mentioned models: existence and uniqueness of solutions, self-similar analysis, energy estimates (both in space and time), asymptotic behavior in space and time with rate of convergence to stationary states, positivity estimates and speed of propagation of the support, existence of special solutions (self similar solutions, traveling waves, etc).

My Bachelor and Master studies were accomplished at the University of Bucharest and the Superior Normal School of Bucharest (hosted by the Institute of Mathematics "Simion Stoilow" of the Romania Academy), Romania. In the forthcoming years I had several collaborations with these institutions through short fellowships and research visits.

I graduated the PhD studies in 2014 at the Universidad Autonoma de Madrid. My Ph.D. thesis is entitled Nonlinear and Nonlocal Diffusion Equations under the direction of Professor Juan Luis Vázquez. The thesis concerns of the investigation of three different models of partial differential equations:
1) The Doubly Nonlinear difusion equation.
2) The Fisher-KPP equation with nonlinear fractional diffusion
3) The porous Medium equation with nonlocal pressure.
The results obtained on these topics were published in several research papers as described in section Publications.

Collaborators: Juan Luis Vázquez, Matteo Bonforte (UAM Madrid, Spain), Liviu Ignat (IMAR Romania), Luis Vega (BCAM), Gianni Pagnini (BCAM), Félix del Teso (BCAM).

My publications can be found on the google scholar page: here

Eusko Jaurlaritza - Gobierno Vasco ikerbasque - Basque Foundation for Science Bizkaia xede. Bizkaiko Foru Aldundia innobasque - Agencia vasca de la innovación Universidad del PaÃŒs Vasco (UPV/EHU)