Progress in Partial Differential Equations of Mathematical Physics: Theory and Methods
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Organizer(s): |
Name:
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Affiliation:
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Country:
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Andreas Chatziafratis
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National and Kapodistrian University of Athens
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Greece
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Spyridon Kamvissis
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University of Crete
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Greece
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Tohru Ozawa
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Waseda University
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Japan
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Introduction:
| | The central theme of this session is the rigorous study of initial and of boundary value problems for (systems of) linear and nonlinear equations which arise in mathematical physics. Cutting-edge methods for the analysis of PDE that will be discussed mostly draw on tools from complex, harmonic and functional analysis and potential theory. A diverse array of select scholars shall present state-of-the-art research results which pertain to asymptotics, instabilities, well-posedness, controllability, analyticity, smoothing and other qualitative properties of solutions. Within this session’s broad scope fit techniques and advances related to scattering, soliton and spectral theory, semi-classical and microlocal analysis, variational and perturbation approaches, Hamiltonian and integrable systems, Lax pairs, Riemann-Hilbert factorization problems, Toda lattices, and so on. Recent developments thanks to the Fokas unified transform method for initial-boundary-value problems for linear and integrable PDE (including, among others, evolution and dispersive equations as well as elliptic ones) on a variety of domains and configurations (e.g. intervals, quarter-planes, non-self-adjoint, moving-boundary and interface problems, nonlocal data, etc.) shall comprise an important component of this session.
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