**Institution**: Consejo Superior de Investigaciones Científicas.

**Position**: Contratado ERC

**Office**: S2 **Phone**:+34 912999 780

**E-mail**: razvan.iagar()icmat.es

#### Biographical Review

Razvan Gabriel Iagar was born in Romania in January 1983. He completed the bachelor degree in Mathematics at the University of Bucharest, Romania, in 2005, and then his Ph. D. in Mathematics at the Universidad Autónoma de Madrid (UAM), in June 2010, with Prof. Juan Luis Vázquez Suárez as Thesis advisor. He had various postdoctoral short stays at the Institute de Mathématiques de Toulouse, France, and at the Institute of Mathematics of the Romanian Academy, Bucharest, Romania, before enjoying a Juan de la Cierva (Spanish) postdoctoral contract at the Universidad de Valencia, between 2012-2014. He is a member of ICMAT since February 2015, with a postdoctoral contract in the framework of the Severo Ochoa project.

His research interest is mainly in the qualitative theory and large time behavior of solutions to Partial Differential Equations of Parabolic Type, with emphasis on equations and models that are either degenerate or singular, and on the influence on the behavior of either reaction or absorption effects. He is also interested in finding special solutions with (usually) physical importance, such as self-similar solutions with special properties (concerning symmetry, concentration at initial time) or traveling waves solutions. He is author of research papers published in international journals such as Adv. in Math., J. Functional Analysis, J. Differential Equations, J. Math Pures Appliquées, Annales Inst. Henri Poincaré, Nonlinearity, J. European Math. Society (JEMS), J. London Math. Society et. al. (see a list below).

#### Research Interest

My research interest is related to nonlinear partial differential equations of parabolic type. More precisely, I am interested in the following specific lines:

---qualitative theory and large time behavior for nonlinear diffusion equations; in particular, understanding the competition between diffusion and absorption or reaction effects, and its influence on the asymptotic profiles;

---obtaining special solutions (such as self-similar solutions with some special behavior, or traveling waves) for different models. These solutions reflect usually the sharp properties of the diffusion, arise naturally in applications and they are good candidates as asymptotic profiles;

---understanding the phenomena of blow-up in finite time for reaction-diffusion equations in non-homogeneous media, that is, where coefficients depending on the independent variable appear in the reaction term;

---finer study of the extinction in finite time for nonlinear fast diffusion equations with absorption.

#### Publications

1. R. Iagar, Ph. Laurençot, *Asymptotic behavior for a singular diffusion equation with gradient absorption*, **J. Differential Equations**, 256 (2014), 2739-2777

2. R. Iagar, S. Moll, *Rotationally symmetric p-harmonic flows from D^2 to S^2: local well-posedness and finite time blow up*, **J. Math Anal. Appl.**, 416 (2014), no. 1, 229-257

3. R. Iagar, A. Sánchez, *Large time behavior for the porous medium equation in a nonhomogeneous medium with critical density*, **Nonlinear Anal.**, 102 (2014), 226-241

4. R. Iagar, Ph. Laurençot, *Eternal solutions to a singular diffusion equation with critical gradient absorption*, **Nonlinearity**, 26 (2013), no. 12, 3169-3195

5. R. Iagar, A. Sánchez, *Asymptotic behavior for the heat equation in nonhomogeneous media with critical density*, **Nonlinear Anal.**, 89 (2013), 24-35

6. R. Iagar, Ph. Laurençot, *Existence and uniqueness of very singular solutions for a fast diffusion equation with gradient absorption*, **J. London Math. Society**, 87 (2013), no. 2, 509-529

7. R. Iagar, S. Moll, *Rotationally symmetric p-harmonic maps from D^2 to S^2*, **J. Differential Equations**, 254 (2013), no. 9, 3928-3956

8. R. Iagar, G. Reyes, A. Sánchez, *Radial equivalence of nonhomogeneous nonlinear diffusion equations*, **Acta Appl. Math.**, 123 (2013), 53-72

9. R. Iagar, Ph. Laurençot, *Positivity, decay and extinction for a singular diffusion equation with gradient absorption*, **J. Functional Analysis**, 262 (2012), no. 7, 3186-3239

10. R. Iagar, Ph. Laurençot, J. L. Vázquez, *Asymptotic behavior of a nonlinear diffusion equation with gradient absorption and critical exponent*, **Interfaces and Free Boundaries**, 13 (2011), no. 2, 271-295

11. M. Bonforte, R. Iagar, J. L. Vázquez, *Local smoothing effects, positivity and Harnack inequalities for the fast p-Laplacian equation*, **Adv. in Math.**, 224 (2010), no. 5, 2151-2215

12. R. Iagar, J. L. Vázquez, *Anomalous large-time behavior of the p-Laplacian flow in an exterior domain in low dimension*, **J. European Math. Society (JEMS)**, 12 (2010), no. 1, 249-277

13. R. Iagar, A. Sánchez, *Radial equivalence and study of self-similarity for two very fast diffusion equations*, **J. Math. Anal. Appl.**, 351 (2009), no. 2, 635-652

14. R. Iagar, J. L. Vázquez, *Asymptotic analysis for the p-Laplacian flow in an exterior domain*, **Ann. Inst. Henri Poincaré Annalyse Non Linéaire**, 26 (2009), no. 2, 497-520

15. R. Iagar, A. Sánchez, J. L. Vázquez, *Radial equivalence for the two basic nonlinear degenerate diffusion equations*, **J. Math. Pures Appl.**, 89 (2008), no. 1, 1-24

**Recent preprints**

1. S. Benachour, R. Iagar, Ph. Laurençot, *Large time behavior for the fast diffusion equation with critical absorption*, Preprint **ArXiv no. 1409.2154**