Ignacio A. Guerra

Ph. D.  Eng. Mathematical Sciences

Assistant professor at the Universidad de Santiago de Chile. Fondecyt  1061110.

Research

I am interested in the study of  differential equations and its applications, in particular, the study of existence of positive solutions for nonlinear elliptic systems,  the study of well-posedness and asymptotic behaviour of solutions of porous media type of equations, conservations laws, and reaction diffusion problems.   An overview of my research is my  PhD. Thesis,(ps, pdf).  My PhD. was obtained at the Technical University Eindhoven. (TU/e) and the research was carried out at the CWI. 

Preprints

•  J. Dávila, L. Dupaigne, I. Guerra, M. Montenegro,  Stable solutions for the bilaplacian with exponential nonlinearity. Submitted.
• M. del Pino, and I Guerra, Ground states of a prescribed mean curvature equation, Submmited.

Publications

• I. A Guerra, Solutions of an elliptic system with a nearly critical exponent, accepted in AIHP
• I. A Guerra, Asymptotic behaviour of a semilinear elliptic system with a large exponent, to appear in JDDE
• P. Clément, M. García-Huidobro, I. Guerra, and  R. Manásevich, On regions of existence and nonexistence of solutions for a system of $p$-$q$-Laplacians. Asymptot. Anal. 48 (2006), no. 1-2, 1--18.
• I. Guerra,  Asymptotic self-similar blow-up for a model of aggregation. Nonlocal elliptic and parabolic problems, 165--188, Banach Center Publ., 66, Polish Acad. Sci., Warsaw, 2004.
• I. A. Guerra, and Mark A. Peletier, Self-Similar blow-up for a diffusion-attraction problem, Nonlinearity 17 (2004) 2137--2162
  
• I. A. Guerra, and T. Nadzieja, Convergence to stationary solutions in a model of self-gravitating systems,  Colloquium Mathematicae. 98 no.1  (2003) 39-47
• P. Biler,  M. Cannone, I. A. Guerra, G. Karch, Global regular and singular solutions for a model of gravitating particles , Math. Ann. 330 no.4 (2004) 693-708
• C. J. van Duijn, I. A. Guerra, and Mark A. Peletier, Global Existence Conditions for a Non-local Problem Arising in Statistical Mechanics, CWI Research Report MAS-R0119 (2001), and   Advances in Differential Equations 9 no.1-2 (2004) 133--158.
• C. J. van Duijn, I. A. Guerra, and Mark A. Peletier, Asymptotic Results for Injection of Reactive Solutes from a Three-Dimensional Well, Journal of Mathematical Analysis and Applications, Vol. 260, pp. 367-383 (2001).
• M. Garcia-Huidobro, I. A. Guerra, and R. Manasevich, Existence of positive radial solutions for a weakly coupled system via blow up , Abstr. Appl. Anal. 3 (1998), no. 1-2, 105--131.

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  CAPDE Center for Analysis of Partial Differential Equations