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Homogenization for a Volterra Equation
SIAM Journal on Mathematical Analysis, 1986A model is given for the nonlinear heat equation in a heterogeneous medium with memory. Its homogenization is carried out in two particular cases (including the linear one).
Hedy Attouch, Alain Damlamian
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Eigenvalues and Nonlinear Volterra Equations
1995This paper is devoted to present a solution to the eigenvalue problem for non-linear Volterra operators having the form $$ Tu(x) = \int_0^x {k(x - s)g(u(s))} ds $$ .
Arias M., Castillo J., SIMOES, Marilda
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International journal of numerical modelling, 2019
In this paper, orthonormal Bernoulli collocation method has been developed to obtain the approximate solution of linear singular stochastic Itô‐Volterra integral equations.
Nasrin Samadyar, Farshid Mirzaee
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In this paper, orthonormal Bernoulli collocation method has been developed to obtain the approximate solution of linear singular stochastic Itô‐Volterra integral equations.
Nasrin Samadyar, Farshid Mirzaee
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1999
In this chapter first we shall follow Meehan and O’Regan [213,215] and present results which guarantee the existence of nonnegative solutions of the Volterra integral equation $$y\left( t \right) = h\left( t \right) - \int_0^t {k\left( {t,s} \right)} g\left( {s,y\left( s \right)} \right)ds,t \in {\text{ }}\left[ 0 \right.
Donal O'Regan +2 more
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In this chapter first we shall follow Meehan and O’Regan [213,215] and present results which guarantee the existence of nonnegative solutions of the Volterra integral equation $$y\left( t \right) = h\left( t \right) - \int_0^t {k\left( {t,s} \right)} g\left( {s,y\left( s \right)} \right)ds,t \in {\text{ }}\left[ 0 \right.
Donal O'Regan +2 more
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On a volterra-skorohod equation
Stochastic Analysis and Applications, 1989The existence of weak solutions is established in i lilbcrt spaces for a stochastic Voltcrra integral equation driven by an abstract Wiener process and a Poisson random ...
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1971
Consider the system $${\rm{A\:x}}\left( {\rm{t}} \right) + {\rm{Bx}}\left( {\rm{t}} \right) = \int_0^{\rm{r}} {{\rm{F}}\left( \theta \right){\rm{x}}\left( {{\rm{t}} - \theta } \right)} {\rm{d}}\theta $$ (15.1) where A,B,F are symmetric n × n matrices and F is continuously differentiable. Let $${\rm{M}} = {\rm{B}} - \int_0^{\rm{r}} {{\rm{F}
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Consider the system $${\rm{A\:x}}\left( {\rm{t}} \right) + {\rm{Bx}}\left( {\rm{t}} \right) = \int_0^{\rm{r}} {{\rm{F}}\left( \theta \right){\rm{x}}\left( {{\rm{t}} - \theta } \right)} {\rm{d}}\theta $$ (15.1) where A,B,F are symmetric n × n matrices and F is continuously differentiable. Let $${\rm{M}} = {\rm{B}} - \int_0^{\rm{r}} {{\rm{F}
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A Volterra Equation with Parameter
SIAM Journal on Mathematical Analysis, 1973We discuss the Volterra integral equation $x'(t) + \lambda \int_0^t {a(t - \tau )x(\tau )d\tau = k,\lambda \geq \lambda _0 > 0} $. We find conditions under which solutions are bounded on $\{ 0 \leq t < \infty \} $, uniformly in $\lambda $. We deduce results on the asymptotic behavior of certain Volterra equations in Hilbert space arising, for example ...
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2011
This chapter is devoted to spectral approximations of the Volterra integral equation (VIE): \(y(t)+\int_{o}^{t}R(t,\tau)y(\tau)=f(t),\,\,t\epsilon[0,T],\)
Li-Lian Wang, Tao Tang, Jie Shen
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This chapter is devoted to spectral approximations of the Volterra integral equation (VIE): \(y(t)+\int_{o}^{t}R(t,\tau)y(\tau)=f(t),\,\,t\epsilon[0,T],\)
Li-Lian Wang, Tao Tang, Jie Shen
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Spectral technique for solving variable‐order fractional Volterra integro‐differential equations
, 2018This article, presented a shifted Legendre Gauss‐Lobatto collocation (SL‐GL‐C) method which is introduced for solving variable‐order fractional Volterra integro‐differential equation (VO‐FVIDEs) subject to initial or nonlocal conditions. Based on shifted
E. H. Doha +3 more
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Journal of Soviet Mathematics, 1979
One presents a survey of the investigations in the theory of Volterra integral equations, reviewed in Ref. Zh. “Mat.” between 1966–1976.
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One presents a survey of the investigations in the theory of Volterra integral equations, reviewed in Ref. Zh. “Mat.” between 1966–1976.
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