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The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the Lie algebra of integro-differential operators with matrix coefficients, extended by evolutions for eigenfunctions and adjoint eigenfunctions of the corresponding spectral problems, is obtained via some special Bäcklund transformation. The connection of this hierarchy with integrable by Lax two-dimensional Davey-Stewartson type systems is studied.
The aim of this note is to indicate how inequalities concerning the integral of on the subsets where |u(x)| is greater than k () can be used in order to prove summability properties of u (joint work with Daniela Giachetti). This method was introduced by Ennio De Giorgi and Guido Stampacchia for the study of the regularity of the solutions of Dirichlet problems. In some joint works with Thierry Gallouet, inequalities concerning the integral of on the subsets where |u(x)| is less than k () or...
Mathematical Subject Classification 2010: 35R11, 42A38, 26A33, 33E12.The method of integral transforms based on using a fractional generalization of the Fourier transform and the classical Laplace transform is
applied for solving Cauchy-type problem for the time-space fractional diffusion equation expressed in terms of the Caputo time-fractional derivative and a generalized Riemann-Liouville space-fractional derivative.
An exploratory study is performed to investigate the use of a time-dependent discrete
adjoint methodology for design optimization of a high-lift wing configuration augmented
with an active flow control system. The location and blowing parameters associated with a
series of jet actuation orifices are used as design variables. In addition, a geometric
parameterization scheme is developed to provide a compact set of design variables
describing the wing...
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