On the Bavrin integro-differential operators and their applications to the solution of functional equations.
Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources
We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources in population dynamics. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. They can be related to the emergence of biological species due to the intra-specific competition and random mutations. Various types of travelling waves are observed.
Principal matrix solutions and variation of parameters for a Volterra integro-differential equation and its adjoint.
Problemi inversi, equazioni quasilineari e semigruppi analitici
Propagation of singularities and maximal functions in the plane.
Properties of eigenfunctions of non-local operators
Remarks on the strong maximum principle for nonlocal operators.
Semilinear integro-differential equations with compact semigroups.
Some spectral properties of the streaming operator with general boundary conditions
This paper deals with the spectral study of the streaming operator with general boundary conditions defined by means of a boundary operator . We study the positivity and the irreducibility of the generated semigroup proved in [M. Boulanouar, L’opérateur d’Advection: existence d’un -semi-groupe (I), Transp. Theory Stat. Phys. 31, 2002, 153–167], in the case . We also give some spectral properties of the streaming operator and we characterize the type of the generated semigroup in terms of the...
Spectral analysis for a class of integral-difference operators: known facts, new results, and open problems.
Spectral properties of non-local uniformly-elliptic operators.
The trajectory-coherent approximation and the system of moments for the Hartree type equation.
The Vlasov equation with strong mangnetic field and oscillating electric field as a model for isotop resonant separation.
Valuation of two-factor options under the Merton jump-diffusion model using orthogonal spline wavelets
This paper addresses the two-asset Merton model for option pricing represented by non-stationary integro-differential equations with two state variables. The drawback of most classical methods for solving these types of equations is that the matrices arising from discretization are full and ill-conditioned. In this paper, we first transform the equation using logarithmic prices, drift removal, and localization. Then, we apply the Galerkin method with a recently proposed orthogonal cubic spline-wavelet...
Wavelet method for option pricing under the two-asset Merton jump-diffusion model
This paper examines the pricing of two-asset European options under the Merton model represented by a nonstationary integro-differential equation with two state variables. For its numerical solution, the wavelet-Galerkin method combined with the Crank-Nicolson scheme is used. A drawback of most classical methods is the full structure of discretization matrices. In comparison, the wavelet method enables the approximation of discretization matrices with sparse matrices. Sparsity is essential for the...
Коэрцитивная разрешимость краевых задач для эллиптических дифференциально-операторных уравнений с оператором в краевых условиях.
Устойчивость восстановления памяти по оператору Дирихле-Неймана.