Study of weak solutions for parabolic equations with nonstandard growth conditions

AbstractThe authors of this paper study the existence and uniqueness of weak solutions of the initial and boundary value problem for ut=div((uσ+d0)|∇u|p(x,t)−2∇u)+f(x,t). Localization property of weak solutions is also discussed

A Singular Boundary Value Problem for the One-Dimensionalp-Laplacian

AbstractThe singular boundary value problem[formula]is studied in this paper whereg(s)=|s|p−2s,p>1. The singularity may appear atu=0 and att=0 ort=1 and the functionfmay be discontinuous. The authors prove that for anyp>1 and for any positive, nonincreasing functionfand nonnegative measurable functionkwith some integrability conditions, the above-mentioned problem has a unique solution. Also, the properties of the solution are discussed in the paper

Existence and Uniqueness Results for a Coupled System of Nonlinear Fractional Differential Equations with Antiperiodic Boundary Conditions

This paper studies the existence and uniqueness of solutions for a coupled system of nonlinear fractional differential equations of order α,β∈(4,5] with antiperiodic boundary conditions. Our results are based on the nonlinear alternative of Leray-Schauder type and the contraction mapping principle. Two illustrative examples are also presented

Effects of carbon sources, oxygenation and ethanol on the production of inulinase by Kluyveromyces marxianus YX01

Inulinase is one of the most important factors in consolidated bioprocessing, which combines enzyme production, inulin saccharification, and ethanol fermentation into a single process. In our study, inulinase production and cell growth of Kluyveromyces marxianus YX01 under different conditions were studied. Carbon source was shown to be significant on the production of inulinase, because the activity of inulinase was higher using inulin as a carbon source compared with glucose or fructose. The concentration of the carbon source had a repressive effect on the activity of inulinase. When the concentration was increased to 60 g/L, inulinase activity was only 50% compared with carbon source concentration of 20 g/L. Enzyme activity was also strongly influenced by aeration rate. It has been shown that the activity of inulinase and cell growth under anaerobic conditions were maintained at low levels, but aeration at 1.0 vvm (air volume/broth volume minute) led to higher activity. Inulinase activity per unit biomass was not significantly different under different aeration rates. Ethanol had a repressive effect on the cell growth. Cells ceased growing when the level of ethanol was greater than 9% (v/v), but ethanol did not affect the activity of secreted inulinase and the enzyme was stable at ethanol concentration up to 15%