We consider a class of endomorphisms which contains a set of piecewise partially hyperbolic skew-products with a non-uniformly expanding base map. The aimed transformation preserves a foliation which is almost everywhere uniformly contracted with …
In this paper, we study the Riemann problem for a 2x2 nonstrictly hyperbolic system with linear damping. We introduce the special time-dependent viscosity to obtain approximate solutions. Therefore, we solve the Riemann problem (1.1)–(1.2) by …
The space L(𝑋,𝑌) stands for the Banach space of all bounded linear operators from X to Y endowed with the operator norm. It is shown that 𝑐0(Γ) embeds into (𝑋,𝑌) if and only if 𝑙∞(Γ) embeds into (𝑋,𝑌) or 𝑐0(Γ) embeds into Y. As a consequence, we …
We consider the generalized Riemann problem for the Suliciu re- laxation system in Lagrangian coordinates and we calculate the first-order ex- pansion given by LeFloch and Raviart to verify our results, then we show the explicit solution for the …
This paper is concerned with a hyperbolic system of conservation laws of Keyfitz-Kranzer type. We show the existence of a delta shock wave solution using the vanishing viscosity method. The obtained solution satisfies the generalized Rankine-Hugoniot …
Let 𝐾(𝑛𝐸;𝐹) (resp. 𝑤(𝑛𝐸;𝐹)) denote the subspace of all 𝑃∈(𝑛𝐸;𝐹) which are compact (resp. weakly continuous on bounded sets). We show that if 𝐾(𝑛𝐸;𝐹) contains an isomorphic copy of 𝑐0, then 𝐾(𝑛𝐸;𝐹) is not complemented in (𝑛𝐸;𝐹). Likewise we show …
In this paper we are concerned with the Hölder regularity of weak solutions of the Cauchy problem for the general degenerate parabolic equations in (1). By using the vanishing viscosity method and the maximun principle some explicit Hölder exponent …
We consider a class of endomorphisms which contains a set of piecewise partially hyperbolic skew-products with a non-uniformly expanding base map. The aimed transformation preserves a foliation which is almost everywhere uniformly contracted with …
In this paper we prove that if E and F are reflexive Banach spaces and G is a closed linear subspace of the space 𝐾(𝐸;𝐹) of all compact linear operators from E into F, then G is either reflexive or non-isomorphic to a dual space. This result …
In this paper we consider the Cauchy problem for a particular non-symmetric Keyfitz-Kranzer type system, by using the vanishing viscosity method coupled with the compensated compactness method we get global bounded entropy weak solutions. The main …