Related papers: On the Hopf-Cole Transform for Control-affine Schr…
We study the optimal boundary regularity of solutions to Dirichlet problems involving the logarithmic Laplacian. Our proofs are based on the construction of suitable barriers via the Kelvin transform and direct computations. As applications…
This manuscript reports the first step towards building a robust and efficient model reduction methodology to capture transient dynamics in a transmission level electric power system. Such dynamics is normally modeled on…
Fluid equations are nonlinear, dissipative, and non-Hamiltonian, which makes their relation to Schr\"odinger evolution and quantum algorithms nontrivial. We derive an exact Eulerian Cole-Hopf-type reformulation of isothermal compressible…
This paper deals with a stochastic optimal feedback control problem for the controlled stochastic partial differential equations. More precisely, we establish the existence of stochastic optimal feedback control for the controlled…
This paper studies the controllability for a Keller-Segel type chemotaxis model with singular sensitivity. Based on the Hopf-Cole transformation, a nonlinear parabolic system, which has first-order couplings, and the coupling coefficients…
In this study, we explore multiple higher-order pole solutions in spinor Bose--Einstein condensates. These solutions are associated with different pairs of higher-order poles of the transmission coefficient in the inverse scattering…
In this study, we examined the supercurrent diode effect (SDE) in mesoscopic superconducting weak links formed by asymmetric Dayem bridges. These planar metallic constrictions, which naturally exhibit Josephsonlike behavior, offer a…
We theoretically propose the occurrence of a quantum spin Hall (QSH) and a second order topological phase transition (TPT) driven by electron-phonon (e-p) coupling in a pseudospin-$1$ fermionic system on an $\alpha$-$T_3$ lattice. Our model…
Using a recently introduced representation of the second order adjoint state as the solution of a function-valued backward stochastic partial differential equation (SPDE), we calculate the viscosity super- and subdifferential of the value…
In this paper we consider an optimal control problem (OCP) for the coupled system of a nonlinear monotone Dirichlet problem with matrix- valued non-smooth controls in coefficients and a nonlinear equation of Ham- merstein type. Since…
Hill functions, dominant in gene regulatory network modeling, carry fundamental limitations: at non-integer cooperativity exponents, routine when fitting dose-response data, derivatives diverge at the origin, complex arithmetic corrupts ODE…
Consider a rigid body ${\mathcal S} \subset {\mathbb R}^3$ immersed in an infinitely extended Navier-Stokes liquid and the motion of the body-fluid interaction system described from a reference frame attached to ${\mathcal S}$. We are…
Reactive flow control has been shown as a promising tool to improve, among other aspects, the aerodynamic characteristics of an aircraft. This paper focuses on the use of reactive flow control to attenuate Tollmien-Schlichting (TS) waves…
Hybrid dynamical systems are systems which posses both continuous and discrete transitions. Assuming that the discrete transitions (resets) occur a finite number of times, the optimal control problem can be solved by gluing together the…
We consider the problem of steering a linear stochastic system between two end-point degenerate Gaussian distributions in finite time. This accounts for those situations in which some but not all of the state entries are uncertain at the…
In this short letter we show that the one dimensional non linear Schr\"odinger equation(NLS)can be solved by a Hopf-Cole transformation which converts it to the Burgers equation in turbulence.
Interactions in electron systems can lead to viscous flows in which correlations allow electrons to avoid disorder scattering, reducing momentum loss and dissipation. We illustrate this behavior in a viscous pinball model, describing…
Collisions are common in many dynamical systems with real applications. They can be formulated as hybrid dynamical systems with discontinuities automatically triggered when states transverse certain manifolds. We present an algorithm for…
This work investigates a class of moving boundary problems related to a nonlinear evolution equation featuring an exponential source term. We establish a connection to Stefan-type problems, for different boundary conditions at the fixed…
This paper presents an explicit solution to decentralized control of a class of spatially invariant systems. The problem of optimal $H_2$ decentralized control for cone causal systems is formulated. Using Parseval's identity, the optimal…