Results 271 to 280 of about 39,241 (326)

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.
openaire   +2 more sources

On the mixed nonlinear integro-differential equations with weakly singular kernel

Computational and Applied Mathematics, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hanane Belhireche, Hamza Guebbai
openaire   +2 more sources

On the Solution of a Volterra Integral Equation with a Weakly Singular Kernel

SIAM Journal on Mathematical Analysis, 1973
The solution $x(t)$ of the Volterra integral equation of the second kind $x(t) = f_1 (t) + \sqrt t f_2 (t) + \int _0^t g(t,s,x(s))(t - s)^{ - {1 / 2}} ds$ is examined. It is shown that $x(t) = u(t) + \sqrt t v(t)$, where $u(t)$ and $v(t)$ are smooth under appropriate smoothness conditions on $f_1 (t)$, $f_2 (t)$ and $g(t,s,x)$ and satisfy a system of ...
de Hoog, Frank, Weiss, Richard
openaire   +3 more sources

Solution of a class of Volterra integral equations with singular and weakly singular kernels

Applied Mathematics and Computation, 2008
The purpose of the paper is to derive the solution to a Volterra integral equation \[ y(t)=g(t)+\int^t_0\frac{s^{\mu-\nu}}{t^\mu}y(s)\,ds\quad ...
Bao-Qing Tang, Xian-Fang Li
openaire   +1 more source

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
openaire   +1 more source

Asymptotics on the Fredholm integral equation with a highly oscillatory and weakly singular kernel

Applied Mathematics and Computation, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shuhuang Xiang, Qingyang Zhang
openaire   +1 more source

On the Smoothness of the Solution of Fuzzy Volterra Integral Equations of the Second Kind with Weakly Singular Kernels

, 2021
In this paper. we consider fuzzy Volterra integral equation of the second kind with weakly singular kernel. We prove existence and uniqueness of the solution.
Zahra Alijani, Urve Kangro
semanticscholar   +1 more source

Analysis of a nonlocal diffusion model with a weakly singular kernel

Applied Mathematics Letters
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jinhong Jia, Zhiwei Yang 0008, Hong Wang 0018   +2 more
openaire   +1 more source

On a Nonlinear Volterra Integro‐differential Equation with a Weakly Singular Kernel

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1996
The paper deals with the following heat equation with nonlinear and nonlocal boundary conditions \[ u_t(x,t)=u_{xx}(x,t), \quad x\in(0,1),\;t\in(0,\infty)\quad u(x,0)=1,\;x\in(0,1);\;u_x(0,t) =0,\;t\in(0,\infty) \] \[ u_x(1,t)={Em\over 1+L}\biggl[L\gamma(t)-(1-\gamma(t))u(1,t)\biggr],\;t\in (0,\infty)\quad m\gamma(t)+\int^1_0 u(x,t)dx=1,\;t\in(0,\infty)
Jumarhon, B., Pidcock, M.
openaire   +1 more source

A single-sided all-at-once preconditioning for linear system from a non-local evolutionary equation with weakly singular kernels

Computers and Mathematics with Applications
{In [X. L. Lin, M. K. Ng, and Y. Zhi. {\it J. Comput. Phys.}, 434 (2021), pp. 110221] and [Y. L. Zhao, J. Wu, X. M. Gu, and H. Li. {\it Comput. Math. Appl.}, 148(2023), pp.
Xue-lei Lin, Jiamei Dong, S. Hon
semanticscholar   +1 more source