Related papers: Initial Data Identication in Space Dependent Conse…
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 the inverse design problem for a scalar conservation law, i.e., the problem of finding initial data evolving into a given profile at a given time. The solution we present below takes into account localizations both in the final…
We study the homogenization of first-order Hamilton-Jacobi equations on an infinite-dimensional Hilbert space, motivated by systems of infinitely many indistinguishable particles on the torus. A central difficulty is that the analysis takes…
Here, we study quantitative homogenization of first-order convex Hamilton-Jacobi equations with $(u/\varepsilon)$-periodic Hamiltonians which typically appear in dislocation dynamics. Firstly, we establish the optimal convergence rate by…
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 obtain space-time H\"older regularity estimates for solutions of first- and second-order Hamilton-Jacobi equations perturbed with an additive stochastic forcing term. The bounds depend only on the growth of the Hamiltonian in the…
Various Hamiltonian models have been derived for chemical structures belonging to living organisms while the Hamiltonian concept was not applied to life as a whole. However, Hamiltonian components were recently defined for living organisms…
Motivated by the work of P.L. Lions and J-C. Rochet [12], concerning multi-time Hamilton-Jacobi equations, we introduce the theory of multi-time systems of conservation laws. We show the existence and uniqueness of solution to the Cauchy…
We establish existence and uniqueness of minimax solutions for a fairly general class of path-dependent Hamilton-Jacobi equations. In particular, the relevant Hamiltonians can contain the solution and they only need to be measurable with…
We study well posedness of time--dependent Hamilton--Jacobi equations on a network, coupled with a continuous initial datum and a flux limiter. We show existence and uniqueness of solutions as well as stability properties. The novelty of…
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…
We study a non-local parabolic Lotka-Volterra type equation describing a population structured by a space variable x 2 Rd and a phenotypical trait 2 . Considering diffusion, mutations and space-local competition between the individuals, we…
We study a class of parabolic equations having first order terms with superlinear (and subquadratic) growth. The model problem is the so-called viscous Hamilton-Jacobi equation with superlinear Hamiltonian. We address the problem of having…
In this paper, we study the integrability of contact Hamiltonian systems, both time-dependent and independent. In order to do so, we construct a Hamilton--Jacobi theory for these systems following two approaches, obtaining two different…
We discuss from a bi-Hamiltonian point of view the Hamilton-Jacobi separability of a few dynamical systems. They are shown to admit, in their natural phase space, a quasi-bi-Hamiltonian formulation of Pfaffian type. This property allows us…
The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems…
Systems of Hamilton-Jacobi equations arise naturally when we study the optimal control problems with pathwise deterministic trajectories with random switching. In this work, we are interested in the large time behavior of weakly coupled…
Sharp temporal decay estimates are established for the gradient and time derivative of solutions to a viscous Hamilton-Jacobi equation as well the associated Hamilton-Jacobi equation. Special care is given to the dependence of the estimates…
We show that non-dominated sorting of a sequence of i.i.d. random variables in Euclidean space has a continuum limit that corresponds to solving a Hamilton-Jacobi equation involving the probability density function of the random variables.…