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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 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...
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...
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 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: 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...
Abstract: The main result of the present paper is a statement on existence, uniqueness and regularity for mild solutions to a parabolic transport diffusion type equation that involves a non-smooth coe...
Abstract: 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...
Abstract: Uniqueness results are established for time-independent finite-energy electromagnetic fields which solve the nonlinear Maxwell--Born--Infeld equations in boundary-free space under the condit...
Abstract: Existence and uniqueness of radially symmetric self-similar very singular solutions are proved for the singular diffusion equation with gradient absorption {equation*} \partial_t u -\Delta_{...
Abstract: We prove that radial, monotonic, superexponentially decaying potentials in R^n, n greater than or equal to 1 odd, are determined by the resonances of the associated semiclassical Schrodinger...
Abstract: We consider the zeros distributions on the derivatives of difference polynomials of meromorphic functions, and present some results which can be seen as the discrete analogues of Hayman conj...

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