We show the location of so called critical points, i.e., couples diffusion coefficients for which a non-trivial solution linear reaction-diffusion system activator-inhibitor type on an interval with Neumann boundary conditions and additional non-linear unilateral condition at one or two points and/or in interior exists. Simultaneously, we profile such solutions.

This paper considers the effect of unilateral nonlinearities on the stability of discrete time control systems, a problem of some importance in haptic display. The unilateral nonlinearity is a simple piecewise linear function: ξ(x) = x for x≥0, ξ(x) = 0 for x<0. This function plays an important role in the modeling of collisions, and is a part of essentially all implementations of virtual surfa...

Morphea is an autoimmune connective tissue disease of the dermis and subcutaneous fat characterized by sclerosis due to excessive collagen deposition. Morphea is classified into different subtypes based on clinical and histological characteristics of cutaneous lesions. An extremely rare subtype of morphea is termed unilateral generalized morphea (UGM). UGM is characterized by indurated plaques ...