In this paper a general class of Boltzmann-like bilinear integro-differential systems of equations (GKM, Generalized Kinetic Models) is considered. It is shown that their solutions can be approximated by the solutions of appropriate systems describing the dynamics of individuals undergoing stochastic interactions (at the "microscopic level"). The rate of approximation can be controlled. On the other hand the GKM result in various models known in biomathematics (at the "macroscopic level") including...

In this paper, the initial value problem for the equations of reactor kinetics is solved and the temperature feedback is taken into account. The space where the problem is solved is chosen in such a way that it may correspond best of all to the mathematical properties of the cross-section models. The local solution is found by the method of iterations, its uniqueness is proved and it is shown also that existence of global solution is ensured in the most cases. Finally, the problem of mild solution...

In this paper we discuss the exact null controllability of linear as well as nonlinear Black–Scholes equation when both the stock volatility and risk-free interest rate influence the stock price but they are not known with certainty while the control is distributed over a subdomain. The proof of the linear problem relies on a Carleman estimate and observability inequality for its own dual problem and that of the nonlinear one relies on the infinite dimensional Kakutani fixed point theorem with $L^2$...

In this paper, the linear problem of reactor kinetics with delayed neutrons is studied whose formulation is based on the integral transport equation. Besides the proof of existence and uniqueness of the solution, a special random process and random variables for numerical elaboration of the problem by Monte Carlo method are presented. It is proved that these variables give an unbiased estimate of the solution and that their expectations and variances are finite.

the existence of an $\omega$-periodic solution of the equation $\frac{{\partial }^{2}u}{\partial t^2}+\alpha \frac{{\partial }^{4}u}{\partial x^4}+\gamma \frac{{\partial }^{5}u}{\partial x^4\partial t}-\tilde{\gamma }\frac{{\partial }^{3}u}{\partial x^2\partial t}+\delta \frac{\partial u}{\partial t}-\left[\beta +\aleph {\int }_0^n{\left(\frac{\partial u}{\partial x}\right)}^2(·,\xi )d\xi +\sigma {\int }_0^n\frac{{\partial }^{2}u}{\partial x\partial t}(·,\xi )\frac{\partial u}{\partial x}(·,\xi )d\xi \right]\frac{{\partial }^{2}u}{\partial x^2}=f$ sarisfying the boundary conditions $u(t,0)=u(t,\pi )=\frac{{\partial }^{2}u}{\partial x^2}\left(t,0\right)=\frac{{\partial }^{2}u}{\partial x^2}\left(t,\pi \right)=0$ is proved for every $\omega$-periodic function $f\in C\left(\left[0,\omega \right],L_2\right)$.

This paper concerns $l$-velocity model of the general linear time-dependent transport equation. The assumed probability of the collision (scattering, fission) depends only on the angle of the directions of the moving neutron before and after the collision. The weak formulation of the problem is given and a priori estimates are obtained. The construction of an approximate problem by $bad\; hbox$-method is given. In the symmetric hyperbolic system obtained by $bad\; hbox$-method dissipativity and $𝒜$-orthogonality of the relevant...