Related papers: Singular perturbation results for linear partial d…
An air pollution model is generally described by a system of PDEs on unbounded domain. Transformation of the independent variable is used to convert the problem for nonlinear air pollution on finite computational domain. We investigate the…
We study a Neumann type initial-boundary value problem for strongly degenerate parabolic-hyperbolic equations under the nonlinearity-diffusivity condition. We suggest a notion of entropy solution for this problem and prove its uniqueness.…
We propose a novel framework for model-order reduction of hyperbolic differential equations. The approach combines a relaxation formulation of the hyperbolic equations with a discretization using shifted base functions. Model-order…
We prove some sharp regularity results for solutions of classical first order hyperbolic initial boundary value problems. Our two main improvements on the existing litterature are weaker regularity assumptions for the boundary data and…
An integro-differential equation of hyperbolic type, with mixed boundary conditions, is considered. A continuous space-time finite element method of degree one is formulated. A posteriori error representations based on space-time cells is…
We consider singular perturbations of elliptic systems depending on a parameter ? such that, for ? = 0 the boundary conditions are not adapted to the equation (they do not satisfy the Shapiro - Lopatinskii condition). The limit holds only…
We study small perturbations of the Dirichlet problems for second order elliptic equations that degenerate on the boundary. The limit of the solution, as the perturbation tends to zero, is calculated. The result is based on a certain…
This course introduces the use of semigroup methods in the solution of linear and nonlinear (quasi-linear) hyperbolic partial differential equations, with particular application to wave equations and Hermitian hyperbolic systems. Throughout…
In this paper, we establish a necessary and sufficient stability condition for a class of two coupled first-order linear hyperbolic partial differential equations. Through a backstepping transform, the problem is reformulated as a stability…
Space and time discretizations of parabolic differential equations with dynamic boundary conditions are studied in a weak formulation that fits into the standard abstract formulation of parabolic problems, just that the usual L^2(\Omega)…
In this paper second-order elliptic and parabolic partial differential systems are considered on $C^1$ domains. Existence and uniqueness results are obtained in terms of Sobolev spaces with weights so that we allow the derivatives of the…
This paper studies bulk-surface splitting methods of first order for (semi-linear) parabolic partial differential equations with dynamic boundary conditions. The proposed Lie splitting scheme is based on a reformulation of the problem as a…
Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…
We consider systems of partial differential equations of the form \begin{equation}\nonumber \left\{ \begin{array}{l} u_{xt}=F\left(u,u_x,v,v_x\right),\\ v_{xt}=G\left(u,u_x,v,v_x\right), \end{array} \right. \end{equation} describing…
Motivated by the problem of solving the Einstein equations, we discuss high order finite difference discretizations of first order in time, second order in space hyperbolic systems.Particular attention is paid to the case when first order…
Hyperbolic systems of the first and higher-order partial differential equations appear in many multiphysics problems. We will be dealing with a wave propagation problem in a piece-wise homogeneous medium. Mathematically, the problem is…
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. An analytic function is identified which matches the discontinuity in the initial condition and also satisfies the…
One method for the numerical treatment of future null-infinity is to decouple coordinates from the tensor basis and choose each in a careful manner. This dual-frame approach is hampered by logarithmically divergent terms that appear in a…
We present a spectral method for parabolic partial differential equations with zero Dirichlet boundary conditions. The region {\Omega} for the problem is assumed to be simply-connected and bounded, and its boundary is assumed to be a smooth…
Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…