In this paper, we are concerned with the Cauchy problem on the compressible isentropic two-fluids Euler-Maxwell equations in three dimensions. The global existence of solutions near constant steady states with the vanishing electromagnetic field is established, and also the time-decay rates of perturbed solutions in L space for 2 ≤ q ≤ ∞ are obtained. The proof for existence is due to the class...

for an evolution family (U(t, s))t≤s≤0 on X . We refer to [5, 12] where these equations have been introduced and to [10, 13] for concrete examples. In particular, we showed in [12] that (1.1) and the abstract Cauchy problem associated to an operator ( ,D( )) on the product space := X × L(R−,X) are “equivalent.” Since, under appropriate conditions, the operator ( ,D( )) is the generator of a str...

We prove that the weak solution of the Cauchy problem for the KleinGordon-Zakharov system and for the Zakharov system is unique in the energy space for the former system, and in H×L for the latter system, in dimensions three or lower. These are the largest Sobolev spaces (in three dimensional case) where the local wellposedness has been proven so far. Our proof uses an infinite iteration, where...

In this paper, we have introduced the idea of rough Cauchyness sequences in a cone metric space. We also discussed several basic properties Cauchy space using Phu [8].

We introduce a new method for studying the Cauchy problem for systems of conservation laws in one space dimension. This method is based on the equivalence of the Cauchy problems in Eulerian and Lagrangian coordinates, as regards the existence and uniqueness of entropy solutions. The main idea is to solve the problem in Lagrangian coordinates and determine the transformation linking the two coor...

We study the Cauchy problem for a strictly hyperbolic n × n system of conservation laws in one space dimension

This paper deals with the analysis of a class of doubly nonlinear evolution equations in the framework of a general metric space. We propose for such equations a suitable metric formulation (which in fact extends the notion of Curve of Maximal Slope for gradient flows in metric spaces, see [5]), and prove the existence of solutions for the related Cauchy problem by means of an approximation sch...

This paper is devoted to the study of solutions with critical regularity for two-dimensional Muskat equation. We prove that Cauchy problem well-posed on endpoint Sobolev space $$L^2$$ functions three-half derivative in . result optimal respect scaling One well-known difficulty one cannot define a flow map such lifespan bounded from below subsets this space. To overcome this, we estimate norm wh...

We consider Black-Box continuous optimization by Estimation of Distribution Algorithms (EDA). In continuous EDA, the multivariate Gaussian distribution is widely used as a search operator, and it has the well-known advantage of modelling the correlation structure of the search variables, which univariate EDA lacks. However, the Gaussian distribution as a search operator is prone to premature co...

In this paper, we characterize wellposedness of nonautonomous, linear Cauchy problems (NCP ) { u̇(t) = A(t)u(t) u(s) = x ∈ X on a Banach space X by the existence of certain evolution semigroups. Then, we use these generation results for evolution semigroups to derive wellposedness for nonautonomous Cauchy problems under some “concrete” conditions. As a typical example, we discuss the so called “...