Inverse Problems · 2011 · 271 citations · 32 references
Natural SciencesComputational EngineeringComputational Fluid DynamicsComputational PhysicsDifferential EquationsEigenvalue ProblemsInverse ProblemsInverse Problems In MechanicsLaplace Transform MethodsNumerical Methods For Differential EquationsComputational Inverse ProblemsDiffusion EquationEigenfunction ExpansionsFractional Differential EquationsInverse Diffusion ProblemsInverse Problem TheoryLaplace TransformRegularization
An inverse source problem for a fractional diffusion equation is investigated. Under an assumption that the unknown source term is time independent, an analytical solution can be deduced based on the method of the eigenfunction expansion. Then, the uniqueness of the inverse problem is proved by analytic continuation and Laplace transform. Regularization schemes are considered to obtain the regularized solution. Numerical examples are presented to illustrate the validity and effectiveness of the proposed meshless method.
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