New trends in inverse problems for partial differential equations
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Organizer(s): |
Name:
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Affiliation:
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Country:
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Elena Beretta
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NYUAD
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United Arab Emirates
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Fioralba Cakoni
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Rutgers Univeristy
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USA
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Introduction:
| | Inverse problems for partial differential equations arise in many fields like medical imaging, nondestructive testing of materials, seismology, astronomy, and signal processing to mention but a few.
These are problems where the cause for an observed or desired effect is to be determined.
In many situations, the mathematical modeling of inverse problems is based on linear and nonlinear PDEs and reduces to determine unknown parameters or sources from indirect measurements. A characteristic property of these problems is that they are ill-posed. Therefore, the study of these problems is challenging and it involves techniques from many areas of mathematics and computing such as the analysis of PDEs, micro-local analysis, spectral theory, harmonic analysis, numerical analysis, probability, and machine learning. The field of inverse problems is experiencing tremendous growth leading to many interesting open problems that depend on novel approaches from areas within the discipline of mathematics as well as across different disciplines. In this mini-symposium, we plan to bring together experts working at the forefront of research in inverse problems for PDEs and to focus mainly on inverse problems for nonlinear partial differential equations addressing crucial aspects like uniqueness, stability, and reconstruction.
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