Global existence of solutions to reaction diffusion systems with mass transport type boundary conditions on an evolving domain Vandana Sharma, Jyotshana V. Prajapat Discrete and Continuous Dynamical Systems Series A, 2022 <p style='text-indent:20px;'>We consider reaction diffusion systems where components diffuse inside the domain and react on the surface through mass transport type boundary conditions on an evolving domain. Using a Lyapunov functional and duality arguments, we establish the existence of component wise non-negative global solutions.</p>
Two-and multi-phase quadrature surfaces Avetik Arakelyan, , Henrik Shahgholian, Jyotshana V. Prajapat, , and Communications on Pure and Applied Analysis, 2017 In this paper we shall initiate the study of the two-and multi-phase quadrature surfaces (QS), which amounts to a two/multi-phase free boundary problems of Bernoulli type. The problem is studied mostly from a potential theoretic point of view that (for two-phase case) relates to integral representation \\begin{document}$\\int_{\\partial Ω^+} g h (x) \\ dσ_x - \\int_{\\partial Ω^-} g h (x) \\ dσ_x= \\int h dμ \\ ,$ \\end{document} where \\begin{document} $dσ_x$ \\end{document} is the surface measure, \\begin{document} $μ= μ^+ - μ^-$ \\end{document} is given measure with support in (a priori unknown domain) \\begin{document} $Ω=Ω^+\\cupΩ^-$ \\end{document} , \\begin{document} $g$ \\end{document} is a given smooth positive function, and the integral holds for all functions \\begin{document} $h$ \\end{document} , which are harmonic on \\begin{document} $\\overline Ω$ \\end{document} . Our approach is based on minimization of the corresponding two-and multi-phase functional and the use of its one-phase version as a barrier. We prove several results concerning existence, qualitative behavior, and regularity theory for solutions. A central result in our study states that three or more junction points do not appear.
Taylor expansion for an analytic hypersurface in rn Jyotshana V. Prajapat Taiwanese Journal of Mathematics, 2010 Here we obtain a Taylor’s expansion of the function ρ(x, r) = |B(x,r)| |B(x,r)∩Ω| for r small and x ∈ ∂Ω where the boundary of domain Ω is assumed to be analytic. The coefficients are expressed as recurrence relation and it is proved yhat the series is odd.
Preliminary experiments to evaluate the Gassmann equation in carbonate rocks: Calcite and dolomite S. Vega, J. V. Prajapat, A. A. Al Mazrooei Leading Edge Tulsa OK, 2010 Fluid substitution is used to predict potential changes in seismic data due to production in oil reservoirs. The fluid changes in clastic rocks are often predicted by the Gassmann equation. However, the applicability of Gassmann's equation in carbonates is not well understood. Apparently, part of this failure is due to the violation of the assumption of a constant shear modulus for different fluids (Baechle et al., 2005; Adam et al., 2006), but it is not clear yet.
