An initial-boundary value problem for the one-dimensional non-classical heat equation in a slab
Boundary Value Problems, 2011 Nonlinear problems for the one-dimensional heat equation in a bounded and homogeneous medium with temperature data on the boundaries x = 0 and x = 1, and a uniform spatial heat source depending on the heat flux (or the temperature) on the boundary x = 0 ...
Salva Natalia +2 more
doaj
Optimal control of impulsive Volterra equations with variable impulse times [PDF]
arXiv, 2008 We obtain necessary conditions of optimality for impulsive Volterra integral equations with switching and impulsive controls, with variable impulse time-instants. The present work continues and complements our previous work on impulsive Volterra control with fixed impulse times.
arxiv
Properties of solutions for nonlinear Volterra integral equations [PDF]
, 2003 Some properties of non-locally bounded solutions for Abel integral equations are given. The case in which there exists two non-trivial solutions for such equations is also studied.
Arias, M. R., Benítez Suárez, Rafael
core +1 more source
Fractional White Noise Perturbations of Parabolic Volterra Equations [PDF]
arXiv, 2010 Aim of this work is to extend the results of Cl\'ement, Da Prato & Pr\"uss on the fractional white noise perturbation with Hurst parameter 0
arxiv
Optimal control for stochastic heat equation with memory [PDF]
arXiv, 2011 In this paper, we investigate the existence and uniqueness of solutions for a class of evolutionary integral equations perturbed by a noise arising in the theory of heat conduction. As a motivation of our results, we study an optimal control problem when the control enters the system together with the noise.
arxiv
Solution to the Volterra Operator Equations of the 1st kind with Piecewise Continuous Kernels [PDF]
arXiv, 2012 The sufficient conditions for existence and uniqueness of continuous solutions of the Volterra operator equations of the first kind with piecewise continuous kernel are derived. The asymptotic approximation of the parametric family of solutions are constructed in case of non-unique solution.
arxiv
A series approach to stochastic Volterra equations of convolution time [PDF]
arXiv, 2012 In the paper stochastic Volterra equations with noise terms driven by series of independent scalar Wiener processes are considered. In our study we use the resolvent approach to the equations under consideration. We give sufficient condition for the existence of strong solution to the class of stochastic Volterra equations of convolution type.
arxiv
Temporal and spatial regularity of solutions to stochastic Volterra equations of convolution type [PDF]
arXiv, 2012 In the paper regularity of solutions to stochastic Volterra equations in a separable Hilbert space is studied. Sufficient conditions for the temporal and spatial regularity of stochastic convolutions corresponding to the equations under consideration are provided.
arxiv
Existence and Destruction of Kantorovich Main Continuous Solutions of Nonlinear Integral Equations [PDF]
arXiv, 2013 The sufficient conditions are obtained for existence of the main solution of the nonlinear Volterra integral equation of the second kind on the semi-axis and on a finite interval. The method for computation of this boundary interval is designed. Beyond such integral the solution has the blow-up.
arxiv
Numerical Solution of Weakly Regular Volterra Integral Equations of the First Kind [PDF]
arXiv, 2014 The numerical method for solution of the weakly regular scalar Volterra integral equation of the 1st kind is proposed. The kernels of such equations have jump discontinuities on the continuous curves which starts at the origin. The mid-rectangular quadrature rule is employed. The accuracy of proposed numerical method is $\mathcal{O}(1/N).$
arxiv