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Backward solutions to nonlinear integro-differential systems

100%
Bai Y.
Open Mathematics
|
2010
|
tom 8
|
nr 4
807-815
EN
In this paper, we show the backward uniqueness in time of solutions to nonlinear integro-differential systems with Neumann or Dirichlet boundary conditions. We also discuss reasonable physical interpretations for our conclusions.
2
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Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition

100%
Povstenko Y.
Open Mathematics
|
2014
|
tom 12
|
nr 4
611-622
EN
The central symmetric time-fractional heat conduction equation with Caputo derivative of order 0 < α ≤ 2 is considered in a ball under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of values of temperature and values of its normal derivative at the boundary, and the physical condition with the prescribed linear combination of values of temperature and values of the heat flux at the boundary, which is a consequence of Newton’s law of convective heat exchange between a body and the environment. The integral transform technique is used. Numerical results are illustrated graphically.
3
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Large time behavior of the solution to an initial-boundary value problem with mixed boundary conditions for a nonlinear integro-differential equation

76%
Jangveladze T., Kiguradze Z.
Open Mathematics
|
2011
|
tom 9
|
nr 4
866-873
EN
Large time behavior of the solution to the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. Furthermore, the rate of convergence is given. Initial-boundary value problem with mixed boundary conditions is considered.
4
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Decay rates of Volterra equations on ℝN

76%
Conti M., Gatti S., Pata V.
Open Mathematics
|
2007
|
tom 5
|
nr 4
720-732
EN
This note is concerned with the linear Volterra equation of hyperbolic type $$\partial _{tt} u(t) - \alpha \Delta u(t) + \int_0^t {\mu (s)\Delta u(t - s)} ds = 0$$ on the whole space ℝN. New results concerning the decay of the associated energy as time goes to infinity were established.
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