Journal of Hyperbolic Differential Equations 

About: Journal of Hyperbolic Differential Equations is an academic journal published by World Scientific. The journal publishes majorly in the area(s): Conservation law & Nonlinear system. It has an ISSN identifier of 0219-8916. Over the lifetime, 496 publications have been published receiving 8472 citations. The journal is also known as: JHDE.

Inhomogeneous strichartz estimates

Abstract: We look for the optimal range of Lebesque exponents for which inhomogeneous Strichartz estimates are valid. It is known that this range is larger than the one given by admissible exponents for homogeneous estimates. We prove inhomogeneous estimates in this larger range adopting the abstract setting and interpolation techniques already used by Keel and Tao for the endpoint case of the homogeneous estimates. Applications to Schrodinger equations are given, which extend previous work by Kato.

Global well-posedness of the benjamin–ono equation in h1(r)

Abstract: We show that the Benjamin–Ono equation is globally well-posed in Hs(R) for s≥1. This is despite the presence of the derivative in the nonlinearity, which causes the solution map to not be uniformly continuous in Hs for any s [18]. The main new ingredient is to perform a global gauge transformation which almost entirely eliminates this derivative.

Optimal entropy solutions for conservation laws with discontinuous flux-functions

Abstract: We deal with a single conservation law in one space dimension whose flux function is discontinuous in the space variable and we introduce a proper framework of entropy solutions. We consider a large class of fluxes, namely, fluxes of the convex-convex type and of the concave-convex (mixed) type. The alternative entropy framework that is proposed here is based on a two step approach. In the first step, infinitely many classes of entropy solutions are defined, each associated with an interface connection. We show that each of these class of entropy solutions form a contractive semigroup in L1 and is hence unique. Godunov type schemes based on solutions of the Riemann problem are designed and shown to converge to each class of these entropy solutions. The second step is to choose one of these classes of solutions. This choice depends on the Physics of the problem being considered and we concentrate on the model of two-phase flows in a heterogeneous porous medium. We define an optimization problem on the set of admissible interface connections and show the existence of an unique optimal connection and its corresponding optimal entropy solution. The optimal entropy solution is consistent with the expected solutions for two-phase flows in heterogeneous porous media.

A counterexample to well-posedness of entropy solutions to the compressible Euler system

Abstract: We consider entropy solutions to the Cauchy problem for the isentropic compressible Euler equations in the spatially periodic case. In more than one space dimension, the methods developed by De Lellis–Szekelyhidi enable us to show here failure of uniqueness on a finite time-interval for entropy solutions starting from any continuously differentiable initial density and suitably constructed bounded initial linear momenta.

Existence of strong traces for quasi-solutions of multidimensional conservation laws

Abstract: We consider a conservation law in the domain Ω ⊂ ℝn+1 with C1 boundary ∂Ω. For a wide class of functions including generalized entropy sub- and super-solutions, we prove the existence of strong traces for normal components of the entropy fluxes on ∂Ω. Non-degeneracy conditions on the flux are not required.