Stevan Pilipović, Mirjana Stojanović Abstract. We recall the definition of G–quasiasymptotics at infinity in a framework of Colombeau space G (cf. [8]) and give an application of that notion to a Cauchy problem for a strictly semilinear hyperbolic system. It turns out that quasiasymptotic behaviour at infinity of the solution inherits the quasiasymptotic behaviour at infinity of initial data un...

In this paper we investigate the numerical solution of non-linear equations in an abstract (Banach space) setting. The main result is that the convergence can be guaranteed by two, directly checkable conditions (namely, by the consistency and the stability). We show that these conditions together are a sufficient, but not necessary condition for the convergence. Our theoretical results are demo...

Abstract. In this paper we consider some dissipative versions of the modified Korteweg de Vries equation ut+uxxx+ |Dx| u+uux = 0 with 0 < α ≤ 3. We prove some well-posedness results on the associated Cauchy problem in the Sobolev spaces Hs(R) for s > 1/4−α/4 on the basis of the [k; Z]−multiplier norm estimate obtained by Tao in [9] for KdV equation. 2000 Mathematics Subject Classification: 35Q5...

Abstract. We introduce a concept of viscosity solutions for Hamilton-Jacobi equations (HJE) in the Wasserstein space. We prove existence of solutions for the Cauchy problem for certain Hamiltonians defined on the Wasserstein space over the real line. In order to illustrate the link between HJE in the Wasserstein space and Fluid Mechanics, in the last part of the paper we focus on a special Hami...

Abstract. This Note derives regularity bounds for a Gevrey criterion when the Cauchy problem of elliptic equations is solved by regularization. When utilizing the regularization, one knows that checking such criterion is basically problematic, albeit its importance to engineering circumstances. Therefore, coping with that impediment helps us improve the use of some regularization methods in rea...

In this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional Cauchy problem with an integral initial condition in Banach spaces.

* Correspondence: jinliang@sjtu. edu.cn Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, P. R. China Full list of author information is available at the end of the article Abstract We are concerned with the existence of mild solutions to the Cauchy problem for fractional evolution equations of neutral type with almost sectorial operators dq dtq (x(t) − h(t, x(t))) = −A...