Results 241 to 250 of about 16,231 (283)

Perinatal development of structural thalamocortical connectivity

Oldham S, Mansour L S, Ball G.
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Regularity of the solution of Hammerstein equations with weakly singular kernel

Integral Equations and Operator Theory, 1990
The authors study a class of Fredholm integral equations of the second kind such as \((1)\quad \phi (s)-\int^{b}_{a}g_{\alpha}(| s- t|)k(s,t)\phi (t)dt=f(s),\quad a\leq s\leq b\) where \(g_{\alpha}(s)=s^{\alpha -1}\text{ for ...
Kaneko, Hideaki, Noren, Richard, Xu, Yuesheng   +2 more
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Identification of Weakly Singular Memory Kernels in Viscoelasticity

ZAMM, 1998
The authors deal with the problem of identifying an unknown memory kernel \(m:[0,T]\to {\mathbb{R}}\) in the integrodifferential equation \[ \rho D_t^2u(x,t) - \lambda \text{ div} (\beta \nabla u(x,t)) - (m*\text{ div} (\beta \nabla))(x,t) = \gamma(x,t)\qquad (x,t)\in Q=D\times (0,T) \tag{1} \] where \(\lambda \in \{0,1\}\), \(f*g(t)=\int_0^t f(t-s)g(s)
Janno, J., von Wolfersdorf, L.
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Identification of Weakly Singular Memory Kernels in Heat Conduction

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1997
AbstractInverse problems of identification of memory kernels in linear heat conduction are dealt with in case of weakly singular kernels in the space Lp and of continuous kernels with power singularity. The problems are reduced to nonlinear Volterra integral equations of convolution type for which by the method of contraction with weighted norms global
Janno, J., von Wolfersdorf, Lothar
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A Robust Hybrid Spectral Method for Nonlocal Problems with Weakly Singular Kernels

Numerical Mathematics: Theory, Methods and Applications, 2022
Summary: In this paper, we propose a hybrid spectral method for a type of nonlocal problems, nonlinear Volterra integral equations (VIEs) of the second kind. The main idea is to use the shifted generalized Log orthogonal functions (GLOFs) as the basis for the first interval and employ the classical shifted Legendre polynomials for other subintervals ...
Zhang, Chao, Yao, Guoqing, Chen, Sheng
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Preconditioners for Solving Stochastic Boundary Integral Equations with Weakly Singular Kernels

Computing, 1999
The paper deals with the singular integral equation \[ \sigma(x)= \int_{G'} a(x,y) k(x-y) \sigma(y) dy+ w(x),\tag{1} \] where \(a\in C^m(G'\times G')\), \(k\in C^{m- 1}(G'\setminus\{0\})\), \(m\geq 1\), \(G'\subseteq \mathbb{R}^d\) and \(w\) is a given process defined on a probability space.
Rostami Varnos Fadrani, D., Maleknejad, K.   +1 more
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Nonpolynomial Spline Collocation for Volterra Equations with Weakly Singular Kernels

SIAM Journal on Numerical Analysis, 1983
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Resolvents for weakly singular kernels and fractional differential equations

Nonlinear Analysis: Theory, Methods & Applications, 2012
The resolvent matrix equation \[ R(t,s) = B(t,s) + \int\limits_s^t B(t,u) R(u,s) du, \] where \(B(t,s)\) denotes a given weakly singular matrix is studied. The solution \(R(t,s)\) is obtained by means of fixed point mappings. The result is a series that begins with some singular terms after which the remainder of the terms defines a continuous function.
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Spectral Approximation of Weakly Singular Integrable Kernels Using Projections

2002
As theoretical framework for an integral operator \( T:X \to X \) defined by $$x \mapsto Tx:\tau \in \mathcal{I}: = [0,{{\tau }_{0}}] \mapsto (Tx)(\tau ): = \int_{\mathcal{I}} {g(|\tau - \tau \prime )} x(\tau \prime )d\tau \prime \in \mathbb{C},$$ , with a weakly singular kernel g, we consider \( {\rm X}: = {L^1}(I) \) and we suppose that (a)
Mario Ahues, Olivier Titaud
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