‎in this paper a nonlinear backward parabolic problem in one‎ ‎dimensional space is considered‎. ‎using a suitable iterative‎ ‎algorithm‎, ‎the problem is converted to a linear backward parabolic‎ ‎problem‎. ‎for the corresponding problem‎, ‎the backward finite‎ ‎differences method with suitable grid size is applied‎. ‎it is shown‎ ‎that if the coefficients satisfy some special conditions‎, ‎th...

the release rate of potassium (k) from micaceous minerals plays a significant role in supplying k to plants. the objective of this study was to determine the most appropriate kinetic equation to describe potassium release from micaceous minerals as influenced by organic acids. muscovite and phlogopite were made to react with 0, 500, 2000 and 4000 ?m solutions of oxalic, citric and malic acids f...

Let $f$ be a locally univalent function on the unit disk $U$. We consider the normalized extensions of $f$ to the Euclidean unit ball $B^nsubseteqmathbb{C}^n$ given by $$Phi_{n,gamma}(f)(z)=left(f(z_1),(f'(z_1))^gammahat{z}right),$$  where $gammain[0,1/2]$, $z=(z_1,hat{z})in B^n$ and $$Psi_{n,beta}(f)(z)=left(f(z_1),(frac{f(z_1)}{z_1})^betahat{z}right),$$ in which $betain[0,1]$, $f(z_1)neq 0$ a...

The aim of this paper is to construct the parabolic version of the Donaldson–Uhlenbeck compactification for the moduli space of parabolic stable bundles on an algenraic surface with parabolic structures along a divisor with normal crossing singularities. We prove the non–emptiness of the moduli space of parabolic stable bundles of rank 2 and also prove the existence of components with smooth po...

These notes contain a short exposition of selected results about parabolic equations: Schauder estimates for linear parabolic equations with Hölder coefficients, some existence, uniqueness and regularity results for viscosity solutions of fully nonlinear parabolic equations (including degenerate ones), the Harnack inequality for fully nonlinear uniformly parabolic equations. MSC. 35K55, 35D40, ...

introduction coastal sand dunes are  important morphological forms in caspian coastal regions. these dunes are formed and developed under the influence of sediment influx, climate, impact of wind, waves, currents. these are parallel to the coastal characterisitics with enough space for expansion. the whole collection of these parameters are available in many coastal areas of the caspian sea , b...

It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse prob...

Parabolic triples of the form (E∗, θ, σ) are considered, where (E∗, θ) is a parabolic Higgs bundle on a given compact Riemann surface X with parabolic structure on a fixed divisor S, and σ is a nonzero section of the underlying vector bundle. Sending such a triple to the Higgs bundle (E∗, θ) a map from the moduli space of stable parabolic triples to the moduli space of stable parabolic Higgs bu...