4 research outputs found
Existence Results for Quasilinear Degenerated Equations vias Strong Convergence of Truncations
Abstract In this paper, we study the existence of entropy solution for quasilinear elliptic equations of the form, is a non-linear term which has a growth condition with respect to ξ and no growth with respect to s, but it satisfies a sign condition on s. key words: Quasilinear elliptic equation, Sobolev spaces with variable exponent, entropy stronglyregular solution, truncations. References [1] Y
Fractional Cauchy problems on bounded domains: survey of recent results
In a fractional Cauchy problem, the usual first order time derivative is
replaced by a fractional derivative. This problem was first considered by
\citet{nigmatullin}, and \citet{zaslavsky} in for modeling some
physical phenomena.
The fractional derivative models time delays in a diffusion process. We will
give a survey of the recent results on the fractional Cauchy problem and its
generalizations on bounded domains D\subset \rd obtained in \citet{m-n-v-aop,
mnv-2}. We also study the solutions of fractional Cauchy problem where the
first time derivative is replaced with an infinite sum of fractional
derivatives. We point out a connection to eigenvalue problems for the
fractional time operators considered. The solutions to the eigenvalue problems
are expressed by Mittag-Leffler functions and its generalized versions. The
stochastic solution of the eigenvalue problems for the fractional derivatives
are given by inverse subordinators