7th ISAAC Congress
7th ISAAC Congress
IV.2. Dispersive Equations
Organisers: F. Hirosawa (Yamaguchi), M. Reissig (Freiberg)
The goal of the session is to discuss the state-of-the-art of qualitative properties of solutions of dispersive equations. Among other things Strichartz decay estimates, Strichartz estimates, and dispersive estimates are of interest. The question of the influence of low regularity coefficients on the well-posedness of the Cauchy problem is another key topic.
IV.1. Pseudo-differential operators
Organisers: L. Rodino (Torino), M. W. Wong (Toronto)
Topics related to pseudo-differential operators such as PDE, geometry, quantisation, wavelet transforms, localisation operators on groups and symmetric domains, mathematical physics, signal and image processing, among others, are the embodiment of the special session.
IV. PArtial Differential Equations
IV.3. Control and Optimisation of Non-linear Evolutionary Systems
Organisers: F. Bucci (Firenze), I. Lasiecka (Virginia)
The session is focused on new developments in the area of well-posedness, optimisation, and control of systems described by evolutionary partial differential equations. These include: non-linear wave and plate equations, Navier-Stokes and Euler equations, non-linear thermoelasticity, viscoelasticity and electromagnetism. Of particular interest to the session are interacting systems that involve PDE's of different type describing the dynamics on two (or more) separate regions with a coupling on an interface between these regions. Particular examples of such systems are: structural acoustic interactions, fluid structure interactions, magnetostructure interactions. These have a wide range of applications that include medicine (diagnostic imaging such as MRI, ultrasound), engineering (noise reduction in an acoustic cavities, control of turbulence), geophysics (reconstruction of seismic data) and others.
Recent years have witnesses rapid development of new mathematical tools in both analysis and geometry that allow to obtain various PDE estimates of inverse type. These are enabling to establish properties such as controllability, reconstruction of the data, stabilisation or optimal feedback control.
IV.4. Nonlinear PDE
Organisers: V. Georgiev (Pisa), T.Ozawa (Tokyo)
The Session intends to discuss various nonlinear partial differential equations in mathematical physics. Among possible arguments the following ones shall be discussed: existence and qualitative properties of the solutions, existence of wave operators and scattering for these problems, stability of solitary waves and other special solutions.
IV.5. Asymptotic and multiscale analysis (BICS Mini-Symposium)
Organisers: I. Kamotski (Bath), V. Smyshlyaev (Bath)
The minisymposium will focus on fundamental analytical issues associated with differential equations (linear and nonlinear, partial or ordinary) with a small parameter and/or multiple scales, and relevant applications. This includes singularly perturbed problems, problems in thin domain or with singular boundaries, homogenization. The applications may include propagation and localization of waves, blow-up phenomena, metamaterials, etc. The relevant analytic issues are convergence and relevant functional spaces, compactness and propagation of oscillations, asymptotic expansions with error bounds, etc.