There exist relatively few equations describing natural phenomena among a great number of partial differential equations (PDEs). This begs the question what mathematical properties differ equations describing physical processes from other possible ones? It appears that large majority of equations of mathematical physics has nontrivial symmetry properties (see a number of examples e.g. in [1]). ...

Let Ω be a bounded smooth domain in R such that for some integer d ≥ 1 its d-th singular cohomology group with coefficients in some field is not zero, then problem

This paper introduces new LM specification procedures to choose between Logistic and Exponential Smooth Transition Autoregressive (ST AR) models and to improve testing for nonlinearities. The selection procedures introduced here are simpler and have better consistency and power properties than those previously available in the literature. These improvements result from analyzing the properties ...

We prove the existence and uniqueness of global solutions for a Cauchy problem associated to a semilinear Klein-Gordon equation in two space dimension. Our result is based on an interpolation estimate with a sharp constant obtained by a standard variational method. Accepted for publication: ... AMS Subject Classifications: ..., ..., ... 1 2 S. Ibrahim, M. Majdoub, and N. Masmoudi

We consider the following semilinear elliptic equation:    −∆u = λeup in B1, u = 0 on ∂B1, (0.1) where B1 is the unit ball in R, d ≥ 3, λ > 0 and p > 0. First, following Merle and Peletier [13], we show that there exists a unique eigenvalue λp,∞ such that (0.1) has a solution (λp,∞,Wp) satisfying lim|x|→0 Wp(x) = ∞. Secondly, we study a bifurcation diagram of regular solutions to (0.1). It f...

Given a Hilbert space (H, 〈·, ·〉), and interval Λ ⊂ (0, +∞) and a map K ∈ C(H,R) whose gradient is a compact mapping, we consider the family of functionals of the type: I(λ, u) = 1 2 〈u, u〉 − λK(u), (λ, u) ∈ Λ×H. As already observed by many authors, for the functionals we are dealing with the (PS) condition may fail under just this assumptions. Nevertheless, by using a recent deformation Lemma ...

Sea ice attenuates waves propagating from the open ocean. Here, we model evolution of energetic unidirectional random in marginal zone with a nonlinear Schrödinger equation, frequency dependent dissipative term consistent current paradigms and recent field observations. The preferential dissipation high components results concurrent downshift spectral peak that leads to less than exponential en...

Error modelling has played a major role in generating post-corrections of analogue to digital converters (ADC). Benefits by using parametric models for post-correction are that they requires less memory and that they are easier to identify for arbitrary signals. However, the parameters are estimated in two steps; firstly, the integral nonlinearity (INL) is estimated and secondly, the model para...

this paper studies the perturbed klein-gordon equation by the aid of several methods of integrability. there are six forms of nonlinearity that are considered in this paper. the parameter domains are thus identified.

Neural mass models are ubiquitous in large scale brain modelling. At the node level they are written in terms of a set of ODEs with a nonlinearity that is typically a sigmoidal shape. Using structural data from brain atlases they may be connected into a network to investigate the emergence of functional dynamic states, such as synchrony. With the simple restriction of the classic sigmoidal nonl...