We prove the existence of a continuous selection of the multivalued map ) η , ξ ( → AF ) η , ξ ( , where AF ) η , ξ ( is the set of all mild solutions of the Cauchy problem x” ∈ Ax + F(t, x) , x (0) = ξ , x (0) = η assuming that F is Lipschitzian with respect to x and A is the infinitesimal generator of a strongly cosine family of linear operators on a Banach space E. AMS 2000 Subject Classific...

n this paper, we apply picard’s iteration method followed by adomian decomposition method to solve a nonlinear singular cauchy problem of euler- poisson- darboux equation. the solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by carroll and showalter (1976)in the solution of singular cauchy problem.

This paper presents a new approach to constructing a meromorphic bundle map between flat vector bundles over a compact Riemann surface having a prescribed Weil divisor (i.e. having prescribed zeros and poles with directional as well as multiplicity information included in the vector case). This new formalism unifies the earlier approach of Ball-Clancey (in the setting of trivial bundles over an...

UAV route planning is the key issue for application of in real-world scenarios. Compared with traditional methods, although intelligent optimization algorithm has stronger applicability and performance, it also problem poor convergence accuracy easy to fall into local optimization. Therefore, an method based on chaotic random opposition-based learning cauchy mutation improved Moth-flame (OLTC-M...

In this paper, we consider the Cauchy problem of system quadratic derivative nonlinear Schrödinger equations introduced by Colin and (2004). We determine an almost optimal Sobolev regularity where smooth flow map exists, except for scaling critical case. This result covers a gap left open in papers first second authors (2014, 2019).

In this paper, we consider the solution map of Cauchy problem to Fokas–Olver–Rosenau–Qiao equation on real line and prove that is not uniformly continuous initial data in Besov spaces. Our result extends previous results Himonas Mantzavinos (Nonlinear Anal 95:499–529, 2014) Li et al. (J Math Fluid Mech 22:50, 2020).

‎we study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎these equations will be converted to a system of‎ ‎singular integral equations with cauchy type kernels‎. ‎using‎ ‎chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of cauchy type singular integral equation which will ...

geospatial information system (gis) has emerged as a very powerful tool for capturing, storing, analyzing, managing, and presenting data that is linked to location. the location information, which is usually obtained from existing maps or the global positioning systems (gps), refers to different coordinate and map projection systems. therefore, unification of the coordinate and mapping systems ...