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MSCA Expressions of Interest 2017

Julian López-Gómez
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Applied Mathematics
Faculty of Mathematical Science
We are one of the leading groups at a World level in the theoretical and numerical analysis of Reaction-Diffusion Equations and Systems, as well as in their applications to Biology, Ecology and Medicine. At present we are extremelly interested in analyzing the effects of spatial and temporal heterogeneities on the dynamics of a number of paradigmatic models in these empirical disciplines. The members of the research team are radicated in three different universities of Madrid, J. Lopez-Gomez and his Ph D Stduents in Complutense University of Madrid, M. Molina-Meyer and her Ph D Students at Carlos III University, Leganés, and S. Cano-Casanova and his Ph D Students at University Pontificia Comillas Madrid. The group maintains fluid contact with some of the very best experts in Nonlinear Analysis, Nonlinear Partial Differential Equations, Reaction-Diffusion Equations and Spatial Ecology, like P. H. Rabinowitz, J. L. M. Mawhin, C. Cosner, R. S. Cantrell, E. N. Dancer, Y. Du, W. M. Ni, Y. Lou, T. Nagai, S. Levin, D. Tilman, H. Berestycki among many others. Some of the students formed in the group enjoied postdoctoral grants in the teams of J. M. Ball (Oxford), H. Brestycki (Paris) and the Normal Superior School of Pisa. The last two books of the group are the following ones:
[B1] J. Lopez-Gomez, Linear Second Order Elliptic Operators, World Scientific Publishing, Singapore 2013. ISBN: 978-981-4440-24-0.
[B2] J. Lopez-Gomez, Metasolutions of Parabolic Equations in Population Dynamics, CRC Press, Boca Raton, Florida, 2015. ISBN: 978-148-2238-98-3.
Among the very last papers published by the membres of the group count the following:
[P1] J. Lopez-Gomez, T. Nagai and T. Yamada, The basin of attraction of the steady-states for a chemotaxis model in R2  with critical mass, J. Funct. Anal. 266 (2014), 3455-3507.
[P11] J. Lopez-Gomez, M. Molina-Meyer and A. Tellini, Complex dynamics caused by facilitation in competitive environments within polluted habitat patches, Eu
The group is very interested in wide areas of mathematics, ranging from Spectral Theory and Linear Algebra, Operator Theory and Degree Theory, up to Nonlinear Partial Differential Equations and Dynamical Systems, as well as applications to Biology, Ecology and Medicine. The title of the last Grant founded by the Spanish Ministry of Economy and Competitivetness is "Nonlinear Elliptic and Parabolic Problems". Among the most concrete problems we are analyzing at present count the following ones:
1.- Analyzing the effects of the spatial heterogeneitites on the dynamics of the diffusive Lotka-Volterra competing species model with special emphasis on the deep question of the problem of the uniqueness.
2.- Ellaboration of numerical models for analyzing the evolution of tumors.
3.- Analyzing the dynamics of superlinear indefinite problems realted to the mean curvature operator.
4.- Analyzing the structure of the nodal solutions in degenerate semilinear boundary value problems.
5.- Characterizing the uniqueness of large solutions in wide classes of semilinear elliptic equations.
6.- Characterizing the dynamics of superlinear indefinite problems under nonlinear boundary conditions.
7.- Analytical construction of a degree for Fredholm mappings from the theory of algebraic multiplicities of Esquinas, Lopez-Gomez, Magnus and Mora-Corral.
8.- Characterizing the existence of Global Smith forms for non-analytic operator pencils.
9. Development of numerical spectral methods for solving nonlinear boundary value problems in planar and spatial domains.
10.- Characterizing the dynamical effects of advective terms in the dynamics of semilinear elliptic parabolic equations.
Mathematics (MAT)
Complete Curriculum vitae
2017-07-15 00:00:00
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