Results 221 to 230 of about 553 (265)

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
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Hanane Belhireche, Hamza Guebbai
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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

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

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
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Shuhuang Xiang, Qingyang Zhang
openaire   +1 more source

PERIODICITY AND SYMMETRY IN A CLASS OF INTEGRAL EQUATIONS WITH WEAKLY SINGULAR KERNELS

Far East Journal of Dynamical Systems, 2023
Summary: We introduce the periodic and symmetric properties of the states in a class of weakly singular integral equations. The motivation of this study is due to the main results reported in a previous paper according to which bounded forces produce bounded states in the infinite field. We observe that within finite time, steady states develop.
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.
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Analysis of a nonlocal diffusion model with a weakly singular kernel

Applied Mathematics Letters
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Jinhong Jia, Zhiwei Yang 0008, Hong Wang 0018   +2 more
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A new degenerate kernel method for a weakly singular integral equation

Applied Mathematics and Computation, 2014
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Hamza Guebbai, Laurence Grammont
openaire   +1 more source