The existence and asymptotic behaviour of solutions of certain class of the integro-differential equations
The existence and exponential stability for random impulsive integrodifferential equations of neutral type.
The Existence of Nontrivial Solutions for a Class of Volterra Equations with Smooth Kernels.
The existence of solutions to a Volterra integral equation
We study the equation u = k∗g(u) with k such that ln k is convex or concave and g is monotonic. Some necessary and sufficient conditions for the existence of nontrivial continuous solutions u of this equation are given.
The expected-projection method: Its behavior and applications to linear operator equations and convex optimization.
The factorization method for cracks in inhomogeneous media
We consider the inverse scattering problem of determining the shape and location of a crack surrounded by a known inhomogeneous media. Both the Dirichlet boundary condition and a mixed type boundary conditions are considered. In order to avoid using the background Green function in the inversion process, a reciprocity relationship between the Green function and the solution of an auxiliary scattering problem is proved. Then we focus on extending the factorization method to our inverse shape reconstruction...
The far-field modelling of transonic compressible flows
We present a method for the construction of artificial far-field boundary conditions for two- and three-dimensional exterior compressible viscous flows in aerodynamics. Since at some distance to the surrounded body (e.g. aeroplane, wing section, etc.) the convective forces are strongly dominant over the viscous ones, the viscosity effects are neglected there and the flow is assumed to be inviscid. Accordingly, we consider two different model zones leading to a decomposition of the original flow...
The Fast Fourier Transform and the Numerical Solution of One-Dimensional Boundary Integral Equations.
The fractional transport equation: an analytical solution and a spectral approximation by Chebyshev polynomials.
The freezing method for Volterra integral equations in a Banach space.
The fundamental solutions for fractional evolution equations of parabolic type.
The Gauss center research in multiscale scientific computation.
The generalized Gronwall inequality and its application to periodic solutions of integrodifferential impulsive periodic system on Banach space.
The generalized Neumann-Poincaré operator and its spectrum [Book]
The grazing collisions asymptotics of the non cut-off Kac equation
The Hopf bifurcation theorem for parabolic equations with infinite delay
The existence of the Hopf bifurcation for parabolic functional equations with delay of maximum order in spatial derivatives is proved. An application to an integrodifferential equation with a singular kernel is given.
The initial value problem for nonlinear Boltzmann equation
The integral equation methods for the perturbed Helmholtz eigenvalue problems.
The interval equation of the nonlinear Fredholm integral equation
The iteration process for the nonlinear two-dimensional oscillation problem.