#### Postdoc Fellow - (Juan de la Cierva 2015)

Linear and Non-Linear Waves
##### Helbidea

Mazarredo, 14. 48009 Bilbao Basque Country - Spain

##### Harremana

Since January 2016, I am Postdoctoral Researcher at the Basque Center of Applied Mathematics in the research area of Analysis of PDEs - Linear and Nonlinear Waves, in the group leaded by Prof. Professor Luis Vega.

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, Relativistic fractional operators),

• 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), unique continuation results of the type Hardy uncertainty principle and strong unique continuation.

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.

** Ph.D.**

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:** Matteo Bonforte (UAM Madrid, Spain), Félix del Teso (NTNU Trondheim Norway), Luis Escauriaza (UPV/EHU Bilbao Spain), Liviu Ignat (IMAR Bucharest Romania), Luz Roncal (BCAM Bilbao Spain), Juan Luis Vázquez (UAM and UCM Madrid Spain), Luis Vega (BCAM).

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

**Publications list: **

** In preparation:**

13. Luis Escauriaza, Diana Stan, in preparation.

12. Luz Roncal, Diana Stan, Luis Vega, in preparation.

11. Matteo Bonforte, Diana Stan, in preparation.

**Submitted:**

10. Diana Stan, Félix del Teso and Juan Luis Vázquez, Existence of solutions for a general porous medium equation with nonlocal pressure, preprint 2016, arXiv:1609.05139.

** Published:**

9. Diana Stan, Félix del Teso and Juan Luis Vázquez, Porous medium equation with nonlocal pressure, in “Current Research in Nonlinear Analysis: In Honor of Haim Brezis and Louis Nirenberg”, Th. Rassias (Ed.), Springer Optimization and Its Applications (SOIA, volume 135), Pages 277–308, 2018.

8. Liviu Ignat and Diana Stan, Asymptotic behaviour of solutions to fractional diffusion-convection equations, J. Lond. Math. Soc. (2) 97 (2018), no. 2, 258-281.

7.Diana Stan, Félix del Teso and Juan Luis Vázquez, Finite and infinite speed of propagation for porous medium equations with nonlocal pressure, Journal of Differential Equations 260 (2), year 2017, 1154–1199.

6. Diana Stan, Félix del Teso and Juan Luis Vázquez, Transformations of Self-Similar Solutions for porous medium equations of fractional type, Nonlinear Analysis Series A: Theory, Methods and Applications, Volume 119, Year 2015, Pages 62–73.

5. Diana Stan and Juan Luis Vázquez, The Fisher-KPP equation with nonlinear fractional diffusion, SIAM J. Math. Anal., Volume 46, no. 5, Year 2014, Pages 3241-3276.

4. Diana Stan, Félix del Teso and Juan Luis Vázquez, Finite and infinite speed of propagation for porous medium equations with fractional pressure, Comptes Rendus Mathematique, Volume 352, Number 2, Year 2014, Pages 123–128.

3. Diana Stan and Juan Luis Vázquez, Asymptotic behaviour of the doubly nonlinear diffusion equation on bounded domains, Nonlinear Analysis Series A: Theory, Methods and Applications, Volume 77,
January 2013, Pages 1-32.

2. Diana Putan and Diana Stan, Dynamical behavior of endomorphisms on certain invariant sets, Mathematica Slovaca, Vol.63 no.1 , Year 2013, Pages 135–142.

1. Liviu Ignat and Diana Stan, Dispersive properties of discrete Schrodinger equations, J. Fourier Anal. Appl. Volume 17, Number 5, Year 2011, Pages 1035-1065.