We revisit the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. We prove that, under some assumption on the control operator, two scalar controls are necessary and sufficient ...
The focus of this work is on the development of an error-driven isogeometric framework, capable of automatically performing an adaptive simulation in the context of second- and fourth-order, elliptic partial differential equations defined on two-dimensiona ...
2020
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This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice---a setting that, as pointed out by Zeng, Leung, Hickernell (MCQMC2004, 2006) and Zeng, Kritzer, Hickernell (C ...
In this work, we consider the approximation of Hilbert space-valued meromorphic functions that arise as solution maps of parametric PDEs whose operator is the shift of an operator with normal and compact resolvent, e.g., the Helmholtz equation. In this res ...
We study the Cauchy problem for the half Ginzburg- Landau-Kuramoto (hGLK) equation with the second order elliptic operator having rough coecients and potential type perturbation. The blow-up of solutions for hGLK equation with non-positive nonlinearity is ...
We consider the null controllability of homogeneous quasilinear hyperbolic systems with one side controls and with nonlinear boundary condition at the other side. We present time-independent feedbacks for the null-controllability for C1-solutions at any ...
We study the regularity of the probability density function of the supremum of the solution to the linear stochastic heat equation. Using a general criterion for the smoothness of densities for locally nondegenerate random variables, we establish the smoot ...
In part I, we address the issue of existence of solutions for Cauchy problems involving nonlinear hyperbolic equations for initial data in Sobolev spaces with scaling subcritical regularity. In particular, we analyse nonlinear estimates for null-forms in t ...
We present a systematic method to expand in components four dimensional superconformal multiplets. The results cover all possible N = 1 multiplets and some cases of interest for N = 2. As an application of the formalism we prove that certain N = 2 spinning ...
Recent technological advances in light-sheet microscopy make it possible to perform whole-brain functional imaging at the cellular level with the use of Ca2+ indicators. The outstanding spatial extent and resolution of this type of data open unique opportu ...