Related papers: Compactness for nonlinear transport equations
This paper introduces a mathematical approach that allows one to numerically solve the nonclassical transport equation in a deterministic fashion using classical numerical procedures. The nonclassical transport equation describes particle…
This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…
In this article, we study a non-Newtonian Stokes-Transport system. This set of PDEs was introduced as a model for describing the behavior of a cloud of particles in suspension in a Stokes fluid, and is a nonlinear coupling between a…
In this paper we present a novel method for the numerical solution of linear transport equations, which is based on ridgelets. Such equations arise for instance in radiative transfer or in phase contrast imaging. Due to the fact that…
We present a well-posedness and stability result for a class of nondegenerate linear parabolic equations driven by rough paths. More precisely, we introduce a notion of weak solution that satisfies an intrinsic formulation of the equation…
We establish local-in-time existence and uniqueness results for nonlocal conservation laws with a nonlinear mobility, in several space dimensions, under weak assumptions on the kernel, which is assumed to be bounded and of finite total…
In this paper by using the measure of noncompactness concept, we present new fixed point theorems for multivalued maps. In further we introduce a new class of mappings which are general than Meir-Keeler mappings. Finally, we use these…
Existence and non-existence results are established for quasilinear elliptic problems with nonlinear boundary conditions and lack of compactness. The proofs combine variational methods with the geometrical feature, due to the competition…
In this note, we introduce some models of pedestrian traffic and prove existence and uniqueness for these models.
We consider localized soliton-like solutions in the presence of a stable scalar condensate background. By the analogy with classical mechanics, it can be shown that there may exist solutions of the nonlinear equations of motion that…
We prove concavity properties for solutions to anisotropic quasi-linear equations, extending previous results known in the Euclidean case. We focus the attention on nonsmooth anisotropies and in particular we also allow the functions…
We establish near-optimal quantitative uniqueness of continuation for solutions of evolution equations vanishing on the lateral boundary. These results were obtained simply by combining existing observability inequalities and energy…
We prove compactness of solutions of a fully nonlinear Yamabe problem satisfying a lower Ricci curvature bound, when the manifold is not conformally diffeomorphic to the standard sphere. This allows us to prove the existence of solutions…
This review is devoted to the different techniques that have been developed to compute the phase-coherent transport properties of quantum nanoelectronic systems connected to electrodes. Beside a review of the different algorithms proposed…
We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic…
Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace's equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in…
We study a class of nonlinear nonlocal conservation laws with discontinuous flux, modeling crowd dynamics and traffic flow, without any additional conditions on finiteness/discreteness of the set of discontinuities or on the monotonicity of…
In this paper we established a class of optimal fourth-order methods which is obtained by existing third-order method for solving nonlinear equations for simple roots by using weight functions. Some physical examples are given to illustrate…
We obtain sufficient conditions for the uniqueness of solutions to the Cauchy problem for the continuity equation in classes of measures that need not be absolutely continuous.
In this paper, we are concerned with a model of polytropic gas flow, which consists the mass equation, the momentum equation and a varying entropy equation. First, a new technique, to set up a relation between the Riemann invariants of the…