相关论文: Localized Inverse Design in Conservation Laws and …
In the scalar 1D case, conservation laws and Hamilton-Jacobi equations are deeply related. For both, we characterize those profiles that can be attained as solutions at a given positive time corresponding to at least one initial datum.…
Recently, results regarding the Inverse Design problem for Conservation Laws and Hamilton-Jacobi equations with space-dependent convex fluxes were obtaine. More precisely, characterizations of attainable sets and the set of initialdata…
Consider a Conservation Law and a Hamilton-Jacobi equation with a ux/Hamiltonian depending also on the space variable. We characterize rst the attainable set of the two equations and, second, the set of initial data evolving at a prescribed…
We study the inverse problem, or inverse design problem, for a time-evolution Hamilton-Jacobi equation. More precisely, given a target function $u_T$ and a time horizon $T>0$, we aim to construct all the initial conditions for which the…
The explicit formulation of the general inverse problem on conservation laws is presented for the first time. In this problem one aims to derive the general form of systems of differential equations that admit a prescribed set of…
The initial boundary value problem for a class of scalar non autonomous conservation laws in one space dimension is proved to be well posed and stable with respect to variations in the flux. Targeting applications to traffic, the regularity…
The paper provides results for the stabilization of a spatially uniform equilibrium profile for a scalar conservation law that arises in the study of traffic dynamics under variable speed limit control. Two different control problems are…
Parameterization (closure) schemes in numerical weather and climate prediction models account for the effects of physical processes that cannot be resolved explicitly by these models. Methods for finding physical parameterization schemes…
For the hyperbolic system of quasilinear first-order partial differential equations, linearizable by hodograph transformation, the conservation laws are used to solve the Cauchy problem. The equivalence of the initial problem for…
Consider two hyperbolic systems of conservation laws in one space dimension with the same eigenvalues and (right) eigenvectors. We prove that solutions to Cauchy problems with the same initial data differ at third order in the total…
This report concerns the inverse problem of estimating a spacially dependent coefficient of a partial differential equation from observations of the solution at the boundary. Such a problem can be formulated as an optimal control problem…
In this contribution, we present a novel approach for solving the obstacle problem for (linear) conservation laws. Usually, given a conservation law with an initial datum, the solution is uniquely determined. How to incorporate obstacles,…
In this article, we present a method to find a solution to a one-dimensional nonlocal conservation law that respects a space-dependent mapping, referred to as the obstacle. This is achieved by generalizing existing results for the local…
We consider a scalar conservation law with a spatially discontinuous flux at a single point $x=0$, and we study the initial data identification problem for $AB$-entropy solutions associated to an interface connection $(A,B)$. This problem…
We address the study of a class of 1D nonlocal conservation laws from a numerical point of view. First, we present an algorithm to numerically integrate them and prove its convergence. Then, we use this algorithm to investigate various…
In the context of optimal control, we consider the inverse problem of Lagrangian identification given system dynamics and optimal trajectories. Many of its theoretical and practical aspects are still open. Potential applications are very…
Inverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the…
An algorithmic method using conservation law multipliers is introduced that yields necessary and sufficient conditions to find invertible mappings of a given nonlinear PDE to some linear PDE and to construct such a mapping when it exists.…
In this paper we present a novel framework for obtaining high-order numerical methods for scalar conservation laws in one-space dimension for both the homogeneous and non-homogeneous case. The numerical schemes for these two settings are…
Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic…