Results 261 to 270 of about 3,163,886 (311)
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A Volterra Equation in Hilbert Space
SIAM Journal on Mathematical Analysis, 1974This paper concerns the asymptotic behavior of the solution of a Volterra equation in Hilbert space. The proof uses spectral decomposition and a result of independent interest on the global dependence on a parameter of the solution of a scalar integro-differential equation.
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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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Positive quadratures for volterra equations
Computing, 1976The present paper deals with discretizations to linear Volterra equations which preserve the possible positivity of the Volterra operator. It is shown that the method must be implicit and e.g. that the repeated trapezoidal rule has this property. It is then shown how this property can be used in studying the asymptotic behaviour of the solutionsx
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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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Floquet Theory for a Volterra Equation
Journal of the London Mathematical Society, 1988The authors discuss periodic solutions of the integrodifferential equation \[ dy(t)/dt=A(t)y(t)+\int^{t}_{0}C(t,s)y(s)ds+f(t), \] relating two different integrability properties of the resolvent to each other.
Becker, L. C. +2 more
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A Volterra Equation with a Nonconvolution Kernel
SIAM Journal on Mathematical Analysis, 1977This paper is concerned with the asymptotic behavior of solutions of the Volterra integral equation \[x(t) + \int_0^t {a(t,\tau )g(x(\tau ))d\tau = f(t)} ,\quad 0 \leqq t < \infty \] If $x(t)$ is a solution of this equation, the limiting values of $g(x(t))$ are given under various sets of hypotheses on the kernel $a(t,\tau )$ and the functions $g(t ...
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On a semilinear volterra integrodifferential equation
Israel Journal of Mathematics, 1980The Volterra integrodifferential equation $$\begin{array}{*{20}c} {u_t (t,x) + \smallint '_0 a(t - s)( - \Delta u(s,x) + f(x,u(s,x)))ds = h(t,x),,} \\ {t > 0,x \in \Omega \subset R^N ,} \\ \end{array} $$ together with boundary and initial conditions is considered.
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On volterra equations of the first kind
Integral Equations and Operator Theory, 1980The existence of a solution β of the equation $$\int_0^t {a(t - s)d\beta (s) = 1, t > 0} $$ is studied under fairly general assumptions on the function a. Sufficient conditions for the measure β to be absolutely continuous or satisfy some additional regularity properties are given. An extension to nonconvolution kernels is also considered.
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On a Nonlinear Hyperbolic Volterra Equation
SIAM Journal on Mathematical Analysis, 1980We study questions of existence, boundedness and asymptotic behavior of the solutions of the initial value problem \[(*)\qquad \begin{array}{*{20}c} {u_t (t,x) - \int_0^t {a (t - s)\sigma (u_x (s,x))_x = f(t,x),\quad 0 < t < \infty ,\quad x \in R.} } \\ {u(0,x) = u_0 (x),\quad x \in R.} \\ \end{array} \] Here $a:R^ + = [0,\infty ) \to R,\sigma :R \to R,
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On Volterra’s Population Equation with Diffusion
SIAM Journal on Mathematical Analysis, 1985Summary: In this paper Volterra's population equation with diffusion for a single, isolated species \(u\) is considered. Generalizing a result of \textit{R. K. Miller} [SIAM J. Appl. Math. 14, 446-452 (1966; Zbl 0161.31901)] it is shown that every nonnegative solution \(u\not\equiv 0\) tends, as \(t\to \infty\), to a spatially homogeneous distribution \
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