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EN
The one-dimensional time-fractional heat conduction equation with heat absorption (heat release) proportional to temperature is considered. The Caputo time-fractional derivative is utilyzed. The fundamental solutions to the Cauchy and source problems are obtained using the Laplace transform with respect to time and the exponential Fourier transform with respect to the spatial coordinate. The numerical results are illustrated graphically.
EN
The time-fractional heat conduction equation with heat absorption proportional to temperature is considered in the case of central symmetry. The fundamental solutions to the Cauchy problem and to the source problem are obtained using the integral transform technique. The numerical results are presented graphically.
EN
The time-fractional advection-diffusion equation with the Caputo time derivative is studied in a layer. The fundamental solution to the Cauchy problem is obtained using the integral transform technique. The logarithmicsingularity term is separated from the solution. Expressions amenable for numerical treatment are obtained. The numerical results are illustrated graphically.
EN
The one-dimensional time-fractional advection-diffusion equation with the Caputo time derivative is considered in a half-space. The fundamental solution to the Dirichlet problem and the solution of the problem with constant boundary condition are obtained using the integral transform technique. The numerical results are illustrated graphically.
EN
The one-dimensional time-fractional advection-diffusion equation with the Caputo time derivative is considered. The fundamental solution to the Cauchy problem is obtained using the integral transform technique. The numerical results are illustrated graphically.
EN
The thermal interactions between the blood vessel and surrounding biological tissue are analyzed. The tissue temperature is described by the Pennes equation, while the equation determining the change of blood temperature along the blood vessel is formulated on the basis of adequate energy balance. These equations are coupled by a boundary condition given at the blood vessel wall. The problem is solved using the hybrid algorithm, this means the temperature field in biological tissue is determined by means of the boundary element method (BEM), while the blood temperature is determined by means of the finite difference method (FDM). In the final part the examples of computations are presented.
EN
In the paper the diffusion equation with temperature - dependent source function describing the heat conduction problem in axisymmetrical domain is considered. The fundamental solution is determined and the results obtained by means of the boundary element method are compared with the analytical solution.
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EN
Elliptic equation with source term dependent on the first derivative of unknown function is considered. To solve this equation by means of the boundary element method the fundamental solution should be known. In the paper the fundamental solutions for 1D,2D and 3D problems are derived.
EN
Parabolic equation with source term dependent on the first derivative of unknown function is considered. To solve this equation by means of the boundary element method the fundamental solution should be known. In the paper the fundamental solution for 3D problem is derived.
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