We study the Mackey-Glass type monostable delayed reaction-diffusion equation with a unimodal birth function \begin{document}$ g(u) $\end{document}. This model, designed to describe evolution of single species populations, is considered here in presence weak Allee effect (<tex-math id="M2"...

Motion of a point charge emitting radiation in an electromagnetic field obeys the Abraham--Lorentz--Dirac equation, with effects reaction or self-force incorporated. This class equations describing backreaction, including also for gravitational Einstein's equation cosmology driven by trace anomaly, contains third-order derivative terms. They are known to have pathologies like possession runaway...

Catalytic isomerization of glucose to fructose by immobilized glucose isomerase in an aqueous-ethanol medium was studied. Using Michaelis-Menten equation and Haldane relationship, the main kinetic parameters were determined: Kmf, Vmf, Kmr, Vmr. By comparing the aqueous-ethanol medium with an aqueous solution, the measured values of Kmr and Kmf were increased in the aqueous-ethanol solution, whi...

We derive the single integrodifferential wave equation for the probability density function of the position of a classical one-dimensional Lévy walk with continuous sample paths. This equation involves a classical wave operator together with memory integrals describing the spatiotemporal coupling of the Lévy walk. It is valid at all times, not only in the long time limit, and it does not involv...

in this work the mathematical model of a spatial pattern inchemical and biological systems is investigated numerically. theproposed model considered as a nonlinear reaction-diffusionequation. a computational approach based on finite difference andrbf-collocation methods is conducted to solve the equation withrespect to the appropriate initial and boundary conditions. theability and robustness o...

Reaction random walk systems are hyperbolic models for description of spatial motion (in one dimension) and reaction of particles. In contrast to reaction diiusion equations particles have nite propagation speed. For parabolic systems invariance results and maximum principles are well known. A convex set is positively invariant if at each boundary point an outer normal is a left eigenvector of ...

We consider the (reaction-coordinate) viscosity dependence of reaction-rate coefficients for the two-dimensional AgmonKosloff surface. We show that rate coefficients calculated from the Agmon-Hopfield sink-Smoluchowski equation are a lower bound, approaching asymptotically the two-dimensional result for fast reactive-mode diffusion. A modified equation, employing an effective potential in the s...

Abstract. We study the phase field method for the volume preserving mean curvature flow. Given an initial data which is a measure-theoretic boundary of a Caccioppoli set with a suitable density bound, we prove the existence of the weak solution for the volume preserving mean curvature flow via the reaction diffusion equation with a nonlocal term. We also show the monotonicity formula for the re...

&lt;p style='text-indent:20px;'&gt;We classify the finite time blow-up profiles for following reaction-diffusion equation with unbounded weight:&lt;/p&gt;&lt;p style='text-indent:20px;'&gt;&lt;disp-formula&gt; &lt;label/&gt; &lt;tex-math id="FE1"&gt; \begin{document}$ \partial_tu = \Delta u^m+|x|^{\sigma}u^p, $\end{document} &lt;/tex-math&gt;&lt;/disp-formula&gt;&lt;/p&gt;&lt;p style='text-inde...

The reliability of different electrode admittance equations in the case of the Ag/Ag I electrode is critically discussed. It is shown that the admittance equation already derived for the' metal arnalgam/metal-Ion reversible electrode reaction coupled with reactant adsorption offers some advantages compared to the admittance equation for the reversible electrode reaction on the metal/metal-ion e...