Radiation transfer in an absorbing layer bounded by a specular reflector
Realization theory methods for the stability investigation of nonlinear infinite-dimensional input-output systems
Realization theory for linear input-output operators and frequency-domain methods for the solvability of Riccati operator equations are used for the stability and instability investigation of a class of nonlinear Volterra integral equations in a Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in a weighted Sobolev space, which has the same stability properties as the Volterra equation.
Recent results on the Boltzmann equation
In the last few years the theory of the nonlinear Boltzmann equation has witnessed a veritable turrent of contributions, spurred by the basic result of DiPerna and Lions. Here we wish to survey these results with particular attention to some recent developments.
Recovering a time- and space-dependent kernel in a hyperbolic integro-differential equation from a restricted Dirichlet-to-Neumann operator.
Reducing increasing monotonicity of kernels.
Reduction of boundary value problem to Possio integral equation in theoretical aeroelasticity.
Refinement type equations: sources and results
It has been proved recently that the two-direction refinement equation of the form can be used in wavelet theory for constructing two-direction wavelets, biorthogonal wavelets, wavelet packages, wavelet frames and others. The two-direction refinement equation generalizes the classical refinement equation , which has been used in many areas of mathematics with important applications. The following continuous extension of the classical refinement equation has also various interesting applications....
Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off.
We show that in the setting of the spatially homogeneous Boltzmann equation without cut-off, the entropy dissipation associated to a function f ∈ L1(RN) yields a control of √f in Sobolev norms as soon as f is locally bounded below. Under this additional assumption of lower bound, our result is an improvement of a recent estimate given by P.-L. Lions, and is optimal in a certain sense.
Regularity for solutions of second-order nonlinear integrodifferential functional equations.
Regularity of solutions of Sobolev type semilinear integrodifferential equations in Banach spaces.
Regularization of one class of difference equations.
Regularization properties of Tikhonov regularization with sparsity constraints.
Regularizing a nonlinear integroparabolic Fokker--Planck equation with space-periodic solutions: existence of strong solutions.
Relaxation lengths and non-negative solutions in neutron transport
Reliability of difference analogues to preserve stability properties of stochastic Volterra integro-differential equations.
Remark on linear equations in Banach space
Remark on some conformally invariant integral equations: the method of moving spheres
Remark on the Fredholm alternative for nonlinear operators with application to nonlinear integral equations of generalized Hammerstein type
Remarks on a nonlinear Volterra equation
Remarks on existence of positive solutions of some integral equations
We study the existence of positive solutions of the integral equation in both and spaces, where and . Throughout this paper is nonnegative but the nonlinearity may take negative values. The Krasnosielski fixed point theorem on cone is used.