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On bilinear kinetic equations. Between micro and macro descriptions of biological populations

Mirosław Lachowicz (2003)

Banach Center Publications

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...

On Cauchy problem for the equations of reactor kinetics.

Jan Kyncl (1989)

Aplikace matematiky

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...

On convergence of quadrature-differences method for linear singular integro-differential equations on the interval

A. I. Fedotov (2001)

Archivum Mathematicum

Here we propose and justify the quadrature-differences method for the full linear singular integro-differential equations with Cauchy kernel on the interval ( - 1 , 1 ) . We consider equations of zero, positive and negative indices. It is shown, that the method converges to exact solution and the error estimate depends on the sharpness of derivative approximation and the smoothness of the coefficients and the right-hand side of the equation.

On exact null controllability of Black-Scholes equation

Kumarasamy Sakthivel, Krishnan Balachandran, Rangarajan Sowrirajan, Jeong-Hoon Kim (2008)

Kybernetika

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 ...

On generalized d'Alembert functional equation.

Mohamed Akkouchi, Allal Bakali, Belaid Bouikhalene, El Houcien El Qorachi (2006)

Extracta Mathematicae

Let G be a locally compact group. Let σ be a continuous involution of G and let μ be a complex bounded measure. In this paper we study the generalized d'Alembert functional equationD(μ)    ∫G f(xty)dμ(t) + ∫G f(xtσ(y))dμ(t) = 2f(x)f(y) x, y ∈ G;where f: G → C to be determined is a measurable and essentially bounded function.

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