Related papers: Transparent numerical boundary conditions for evol…
In this paper, we propose to use the eikonal equation as a boundary condition when advective or normal flow equations in the level set formulation are solved numerically on polyhedral meshes in the three-dimensional domain. Since the level…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
We investigate the Cauchy problem for a quasilinear equation with transport rough input of the form $\mathrm{d} u-\partial_i(a^{ij}(u)\partial_j u)\mathrm{d} t =\mathrm{d} \mathbf{X}_t^i(x)\partial_i u_t,$ $u_0\in L^2$ on the torus $\mathbb…
This paper addresses the well posedness of a dynamical model of perfect plasticity with mixed boundary conditions for general closed and convex elasticity sets. The proof relies on an asymptotic analysis of the solution of a perfect…
Initial-boundary value problems for integrable nonlinear partial differential equations have become tractable in recent years due to the development of so-called unified transform techniques. The main obstruction to applying these methods…
Structured population models are a class of general evolution equations which are widely used in the study of biological systems. Many theoretical methods are available for establishing existence and stability of steady states of general…
We study the statistical properties of stochastic evolution equations driven by space-only noise, either additive or multiplicative. While forward problems, such as existence, uniqueness, and regularity of the solution, for such equations…
We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…
In this work, nonreflecting boundary conditions in generalized three-dimensional curvilinear coordinates are derived, relying on the original analysis that was done in Cartesian two-dimensional coordinates by Giles (AIAA Journal, 28.12,…
We discuss the notion of stability and the choice of boundary conditions for AdS-type space-times and point out difficulties in the construction of Cauchy data which arise if reflective boundary conditions are imposed.
The solution of partial differential equations (PDEs) on complex domains often presents a significant computational challenge by requiring the generation of fitted meshes. The Diffuse Domain Method (DDM) is an alternative which reformulates…
In this paper, we consider an acoustic wave transmission problem with mixed boundary conditions of Dirichlet, Neumann, and impedance type. The transmission interfaces may join the domain boundary in a general way independent of the location…
We study Hamilton-Jacobi equations in [0, +$\infty$) of evolution type with nonlinear boundary conditions of Neumann type in the case where the Hamiltonian is non necessarily convex with respect to the gradient variable. In this paper, we…
We consider a class of Fuchsian equations that, for instance, describes the evolution of compressible fluid flows on a cosmological spacetime. Using the method of lines, we introduce a numerical algorithm for the singular initial value…
We consider a class of wave equations with constant damping and polynomial nonlinearities that are perturbed by small, multiplicative, space-time white noise. The equations are defined on a one-dimensional bounded interval with Dirichlet…
Optimal Dirichlet boundary control for a fractional/normal evolution with a final observation is considered. The unique existence of the solution and the first-order optimality condition of the optimal control problem are derived. The…
In this article we develop a high order accurate method to solve the incompressible boundary layer equations in a provably stable manner.~We first derive continuous energy estimates,~and then proceed to the discrete setting.~We formulate…
Domain decomposition methods are used for approximate solving boundary problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are taken into account in the most complete way in…
Using the continuous limit approximation in the dynamical system we study a nonlinear partial differential equation which corresponds to the generalization of both the Fermi-Pasta-Ulam and the Frenkel-Kontorova models. This generalized…