Related papers: Some techniques on nonlinear analysis and applicat…
A method is presented to construct exactly solvable nonlinear extensions of the Schr\"odinger equation. The method explores a correspondence which can be established under certain conditions between exactly solvable ordinary Schr\"odinger…
Contrary to widespread perception, there is ever since 1994 a unified, general type independent theory for the existence of solutions for very large classes of nonlinear systems of PDEs. This solution method is based on the Dedekind order…
We undertake a systematic review of some results concerning local well-posedness of the Cauchy problem for certain systems of nonlinear wave equations, with minimal regularity assumptions on the initial data. Moreover we provide a…
We consider a time-fractional parabolic equation of doubly nonlinear type, featuring nonlinear terms both inside and outside the differential operator in time. The main nonlinearities are maximal monotone graphs, without restrictions on the…
We elucidate a close connection between the Theory of Judgment Aggregation (more generally, Evaluation Aggregation), and a relatively young but rapidly growing field of universal algebra, that was primarily developed to investigate…
A unified treatment is given of low-weight modular forms on \Gamma_0(N), N=2,3,4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations,…
This paper investigates summability principles for multilinear summing operators. The main result presents a novel inclusion theorem for a class of summing operators, which generalizes several classical results. As applications, we derive…
Slowly convergent series and sequences as well as divergent series occur quite frequently in the mathematical treatment of scientific problems. In this report, a large number of mainly nonlinear sequence transformations for the acceleration…
In this paper we address the question of the pointwise almost everywhere limit of nonlinear Schr\"odinger flows to the initial data, in both the continuous and the periodic settings. Then we show how, in some cases, certain smoothing…
Electronics has changed greatly during recent decades, and some its basic concepts should be revisited. Starting from the sampling procedure, we consider some mathematical, physical and engineering aspects related to singular, mainly…
High-dimensional systems that have a low-dimensional dominant behavior allow for model reduction and simplified analysis. We use differential analysis to formalize this important concept in a nonlinear setting. We show that dominance can be…
In part I we introduced modified Landweber-Kaczmarz methods and have established a convergence analysis. In the present work we investigate three applications: an inverse problem related to thermoacoustic tomography, a nonlinear inverse…
In this paper, we study inverse boundary problems associated with semilinear parabolic systems in several scenarios where both the nonlinearities and the initial data can be unknown. We establish several simultaneous recovery results…
We present numerical techniques based on generalized functions adapted to nonlinear calculations. They concern main numerical engineering problems ruled by-or issued from-nonlinear equations of continuum mechanics. The aim of this text is…
Linear systems of neutral type are considered using the infinite dimensional approach. The main problems are asymptotic, non-exponential stability, exact controllability and regular asymptotic stabilizability. The main tools are the moment…
We prove bilinear inequalities for differential operators in $\mathbb{R}^2$. Such type inequalities turned out to be useful for anisotropic embedding theorems for overdetermined systems and the limiting order summation exponent. However,…
In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with…
The purpose of the present work is to study the existence of solutions to initial value problems for nonlinear first order differential systems with nonlinear nonlocal boundary conditions of functional type. The existence results are…
Recent advances in our understanding of higher derived limits carry multiple implications in the fields of condensed and pyknotic mathematics, as well as for the study of strong homology. These implications are thematically diverse,…
We consider a nonlinear semi-classical Schrodinger equation for which it is known that quadratic oscillations lead to focusing at one point, described by a nonlinear scattering operator. If the initial data is an energy bounded sequence, we…