The analytical solution for sediment reaction and diffusion equation with generalized initial-boundary conditions

2001 ◽  
Vol 22 (4) ◽  
pp. 404-408 ◽  
Author(s):  
Xiong Yue-shan ◽  
Onyx Wai Wing hong
Keyword(s):  
Analytical Solution ◽  
Diffusion Equation ◽  
Boundary Conditions ◽  
Initial Boundary ◽  
And Diffusion ◽  
Reaction And Diffusion

An Analytical Solution for Exciton Generation, Reaction, and Diffusion in Nanotube and Nanowire-Based Solar Cells

2016 ◽  
Vol 7 (14) ◽  
pp. 2683-2688 ◽  
Author(s):  
Darin O. Bellisario ◽  
Joel A. Paulson ◽  
Richard D. Braatz ◽  
Michael S. Strano
Keyword(s):  
Solar Cells ◽  
Analytical Solution ◽  
And Diffusion ◽  
Reaction And Diffusion

scholarly journals An Analytical Solution for Effect of Magnetic Field and Initial Stress on an Infinite Generalized Thermoelastic Rotating Nonhomogeneous Diffusion Medium

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
S. R. Mahmoud
Keyword(s):  
Magnetic Field ◽  
Relaxation Time ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Initial Stress ◽  
Chemical Potential ◽  
Thermoelastic Diffusion ◽  
Generalized Thermoelastic ◽  
Analytical Expressions ◽  
And Diffusion

The problem of generalized magneto-thermoelastic diffusion in an infinite rotating nonhomogeneity medium subjected to certain boundary conditions is studied. The chemical potential is also assumed to be a known function of time at the boundary of the cavity. The analytical expressions for the displacements, stresses, temperature, concentration, and chemical potential are obtained. Comparison was made between the results obtained in the presence and absence of diffusion. The results indicate that the effect of nonhomogeneity, rotation, magnetic field, relaxation time, and diffusion is very pronounced.

scholarly journals An Analytical Solution Of 1-D Pseudo Homoneneous Model For Oxidation Reaction Using Homotopy Perturbation Method

2019 ◽  
Vol 1 (1) ◽  
pp. 7-12
Author(s):  
Aang Nuryaman
Keyword(s):  
Analytical Solution ◽  
Diffusion Equation ◽  
Boundary Conditions ◽  
Oxidation Reaction ◽  
Reaction Rate ◽  
Homotopy Perturbation Method ◽  
Convective Diffusion ◽  
Initial Condition ◽  
Homotopy Perturbation ◽  
Convective Diffusion Equation

In this paper, we propose an analytical solution of convective-diffusion equation that derived from an oxidation reaction in a chemical reactor. Here, concentration of feed gas as dependent variable. In this study, the reaction are assumed to be a one-dimensional pseudo homogeneous model and it is evaluated at a certain reaction rate. By rescaling process, the nonlinear term of the reaction rate can be approximated by a linear term, resulting a linear convective-diffusion equation with an initial condition and a set of boundary conditions. Here, we present an analytic solution of the initial condition and the boundary conditions using the homotopy perturbation method. The results show that at the end of the reactor, the solution is in agreement with numerical solution of the initial and boundary conditions.

ON THE SOLVABILITY OF A MIXED PROBLEM WITH DEGREE LAPLACE OPERATORS WITH NONLOCAL BOUNDARY CONDITIONS

2020 ◽  
pp. 85-104
Author(s):  
Shakirbai G. Kasimov ◽  
◽  
Mahkambek M. Babaev ◽  
◽  
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlocal Boundary Conditions ◽  
Laplace Operators ◽  
Initial Boundary Problem ◽  
Initial Boundary Value ◽  
Delayed Time

The paper studies a problem with initial functions and boundary conditions for partial differential partial equations of fractional order in partial derivatives with a delayed time argument, with degree Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes. The solution of the initial boundary-value problem is constructed as the series’ sum in the eigenfunction system of the multidimensional spectral problem. The eigenvalues are found for the spectral problem and the corresponding system of eigenfunctions is constructed. It is shown that the system of eigenfunctions is complete and forms a Riesz basis in the Sobolev subspace. Based on the completeness of the eigenfunctions system the uniqueness theorem for solving the problem is proved. In the Sobolev subspaces the existence of a regular solution to the stated initial-boundary problem is proved.

scholarly journals An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions

2021 ◽  
Vol 5 (3) ◽  
pp. 63
Author(s):  
Emilia Bazhlekova
Keyword(s):  
Boundary Conditions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Stability Estimates ◽  
Inverse Source Problem ◽  
Time Data ◽  
Final Time ◽  
Generalized Eigenfunction ◽  
The One ◽  
Initial Boundary Value

An initial-boundary-value problem is considered for the one-dimensional diffusion equation with a general convolutional derivative in time and nonclassical boundary conditions. We are concerned with the inverse source problem of recovery of a space-dependent source term from given final time data. Generalized eigenfunction expansions are used with respect to a biorthogonal pair of bases. Existence, uniqueness and stability estimates in Sobolev spaces are established.

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