Related papers: Transport-collapse scheme for scalar conservation …
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…
In this paper, we study an initial boundary value problem for a generalized Camassa-Holm equation. We establish local well-posedness of this closed-loop system by using Kato theorem for abstract quasilinear evolution equation of hyperbolic…
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…
Consider a scalar conservation law with discontinuous flux \begin{equation*}\tag{1} \quad u_{t}+f(x,u)_{x}=0, \qquad f(x,u)= \begin{cases} f_l(u)\ &\text{if}\ x<0,\\ f_r(u)\ & \text{if} \ x>0, \end{cases} \end{equation*} where $u=u(x,t)$ is…
We consider a conservation law model of traffic flow, where the velocity of each car depends on a weighted average of the traffic density $\rho$ ahead. The averaging kernel is of exponential type: $w_\varepsilon(s)=\varepsilon ^{-1}…
This paper studies the Cauchy problem for variable coefficient weakly hyperbolic first order systems of partial differential operators. The hyperbolicity assumption is that for each $t, x$ the principal symbol is hyperbolic. No hypothesis…
In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are…
In this work, we propose a novel framework for the numerical solution of time-dependent conservation laws with implicit schemes via primal-dual hybrid gradient methods. We solve an initial value problem (IVP) for the partial differential…
This paper discusses a connection between scalar convex conservation laws and Pontryagin's minimum principle. For flux functions for which an associated optimal control problem can be found, a minimum value solution of the conservation law…
We consider initial boundary-value problems for nonlinear systems of conservation laws in one space variable. It is known that in general different viscous mechanisms yield different solutions in the zero-viscosity limit. Here we focus on…
In this paper we propose a method to couple two or more explicit numerical schemes approximating the same time-dependent PDE, aiming at creating new schemes which inherit advantages of the original ones. We consider both advection equations…
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 paper we study a numerical implementation for the initial boundary value formulation for the generalized conformal field equations. We propose a formulation which is well suited for the study of the long-time behaviour of perturbed…
This paper is concerned with the initial boundary value problem for a nonconservative system of hyperbolic equation appearing in elastodynamics in the space time domain $x > 0, t > 0$. The number of boundary conditions to be prescribed at…
We examine initial-boundary value problems for diffusion equations with distributed order time-fractional derivatives. We prove existence and uniqueness results for the weak solution to these systems, together with its continuous dependency…
A formulation of the boundary integral method for solving partial differential equations has been developed whereby the usual weakly singular integral and the Cauchy principal value integral can be removed analytically. The broad…
A boundary value problem for a fractional power of the second-order elliptic operator is considered. It is solved numerically using a time-dependent problem for a pseudo-parabolic equation. For the auxiliary Cauchy problem, the standard…
In many recent applications when new materials and technologies are developed it is important to describe and simulate new nonlinear and nonlocal diffusion transport processes. A general class of such models deals with nonlocal fractional…
We establish existence and uniqueness of generalized solutions to the initial-boundary value problem corresponding to an Euler-Bernoulli beam model from mechanics. The governing partial differential equation is of order four and involves…
We consider the scalar conservation law in one space dimension with a genuinely nonlinear flux. We assume that an appropriate velocity function depending on the entropy solution of the conservation law is given for the comprising particles,…