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In this paper, we first formulate a linear quasi-static poroelastic shell model of Naghdi's type. The model is given in three unknowns: displacement [ABSTRACT FROM AUTHOR]

This paper deals with the problem of finding minimum-norm fixed point of nonexpansive mappings. We present two types of iteration methods (one is implicit, and the other is explicit). We establish strong convergence theorems for both methods. Some applications are given regarding convex optimization problems and split feasibility problems. These results improve some known results existing in the literatures. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

When adjoint eigenfunctions are adopted as the test functions in Green's second identity for the Euler‐Bernoulli beam equation, we can develop a quite simple noniterative numerical algorithm to recover an unknown space‐dependent external force H(x) exerted on the beam. The spatial parts of the adjoint eigenfunctions are used as the bases to expand the unknown function H(x), where we view the two end values of H(x) as two unknown coefficients for the simply supported and hinged‐clamped beams, and the left end value of H(x) as an unknown coefficient for the cantilevered beam. We can derive closed‐form solutions of the expansion coefficients, and thus closed‐form series solutions of H(x). Consequently, we have a noniterative method to recover the unknown force H(x) supplemented by the noisy final time displacement data. Numerical examples demonstrate the accuracy, efficiency, and robustness of the novel methods in the recovery of unknown forces on the simply supported, cantilevered, and hinged‐clamped beams. [ABSTRACT FROM AUTHOR]

Time-dependent PDEs with fractional Laplacian ( − Δ) α play a fundamental role in many fields and approximating ( − Δ) α usually leads to ODEs' system like u ′( t) + A u( t) = g( t) with A = Q α, where [ABSTRACT FROM AUTHOR]