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Compressible Euler equations are a typical system of hyperbolic conservation laws, whose solution forms shock waves in general. It is well known that global BV solutions of system of hyperbolic conser...
We will talk about our recent results on the convexity, uniqueness, and stability of regular reflection solutions for the potential flow equation in a natural class of self-similar solutions. The appr...
We consider Navier-Stokes equations for compressible viscous fluids in one dimension. It is a well known fact that if the initial datum are smooth and the initial density is bounded by below by a posi...
This paper shows new proof of non-uniqueness of the solution for the retrieving of a compact-supported function starting from a finite number of samples of its spectrum. As will be shown, this is rele...
We show that the set of diagonal similarity scalings that minimize the scaled singular value of a matrix is nonempty and bounded if and only if the matrix that is being scaled is irreducible. For an i...
In this paper, we prove an uniqueness theorem for a n-th order elliptic equation on the standard n-sphere Sn. The problem arises naturally from the point of view of conformal geometry. The method we u...
Let p be a prime, P a finite p-group and F a Frobenius P-category. The question on the existence of a suitable category L^sc extending the full subcategory of F over the set of F-selfcentralizing subg...
The lasso is a popular tool for sparse linear regression, especially for problems in which the number of variables p exceeds the number of observations n. But when p>n, the lasso criterion is not stri...
The paper is devoted to the proof of the uniqueness theorem for solution of the equation for the non-local ionization source in a glow discharge and a hollow cathode in general 3D geometry. The theore...
As we known that there may be more than one solution for backward stochastic differential equation with continuous coefficients and the comparison theorem for any solutions of two BSDEs does not hold ...
In this paper we investigate a kind of generalized Ricci flow which possesses a gradient form. We study the monotonicity of the given function under the generalized Ricci flow and prove that the relat...
Abstract: We use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system. Our proof extends the method used by Loeper in...
Abstract: We show, for mean curvature flows in Euclidean space, that if one of the tangent flows at a given spacetime point consists of a closed, multiplicity-one, smoothly embedded self-similar shrin...
Abstract: In a general spacetime, the possible choices for the field of orthonormal tetrads lead (in standard conditions) to equivalent Dirac equations. However, the Hamiltonian operator is got from r...
Abstract: This article is concerned with the representation of curves by means of integral invariants. In contrast to the classical differential invariants they have the advantage of being less sensit...

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