3 research outputs found
Editorial: Entropic aspects of nonlinear partial differential equations: Classical and quantum mechanical perspectives
There has been increasing research activity in recent years concerning the properties and the applications of nonlinear partial differential equations that are closely related to nonstandard entropic functionals, such as the Tsallis and Renyi entropies. It is well known that some fundamental partial differential equations of applied mathematics and of mathematical physicsâsuch as the linear diffusion equationâare closely linked to the standard, logarithmic BoltzmannâGibbsâShannonâJaynes entropic measure.Facultad de Ciencias Exacta
Editorial: Entropic aspects of nonlinear partial differential equations: Classical and quantum mechanical perspectives
There has been increasing research activity in recent years concerning the properties and the applications of nonlinear partial differential equations that are closely related to nonstandard entropic functionals, such as the Tsallis and Renyi entropies. It is well known that some fundamental partial differential equations of applied mathematics and of mathematical physicsâsuch as the linear diffusion equationâare closely linked to the standard, logarithmic BoltzmannâGibbsâShannonâJaynes entropic measure.Facultad de Ciencias Exacta
Existence of Solutions to a Nonlinear Parabolic Equation of Fourth-Order in Variable Exponent Spaces
This paper is devoted to studying the existence and uniqueness of weak solutions for an initial boundary problem of a nonlinear fourth-order parabolic equation with variable exponent v t + div ( | â â” v | p ( x ) â 2 â â” v ) â | â” v | q ( x ) â 2 â” v = g ( x , v ) . By applying Leray-Schauderâs fixed point theorem, the existence of weak solutions of the elliptic problem is given. Furthermore, the semi-discrete method yields the existence of weak solutions of the corresponding parabolic problem by constructing two approximate solutions