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Partial differential Equations, Numerics and Control

Our main research efforts are oriented towards the analytical understanding and numerical simulation of phenomena and processes in physics and engineering involving, as models, Partial Differential Equations (PDE). In particular, we analyze wave propagation and vibrations of complex mechanical structures, the multiscale modeling for phase transitions in elastically deformable solids and the nonlinear hyperbolic and parabolic problems describing the propagation of nonlinear wave pulses.

From a numerical analysis viewpoint we are mainly concerned with developing efficient numerical methods that mimic the qualitative properties of the continuous models under consideration and in particular, their dispersive and propagation properties, special solutions and nonlinear structures and asymptotic structure as time tends to infinity, which are of primary importance when considering, in particular, control and design problems which are also a primary goal for us. Our work is motivated by applications in shape design in aeronautics and nanomechanisms and nonlinear wave propagation on networks.

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