This paper considers an inverse problem of shear stiffness imaging in a linear isotropic two-dimensional acoustic media, where the targeted parameter is the shear modulus μ. For given single component displacement data, the mathematical model to recover the shear modulus appears to be a first-order partial differential equation while a much simpler algebraic model, called the direct inversion, ...

In this study, for solving the three-dimensional partial differential equation ut = uxx + uyy + uzz, an efficient parallel method based on the modified incomplete Cholesky preconditioned conjugate gradient algorithm (MICPCGA) on the GPU is presented. In our proposed method, for this case, we overcome the drawbacks that the MIC preconditioner is generally difficult to be parallelized on the GPU ...

We study the solvability in Sobolev spaces of problem recovering coefficients right-hand side, or external influence, first order hyperbolic differential equations. Such problems belong to class linear inverse for partial For under study,  we prove existence and uniqueness theorems regular solutions (having all generalized Sobolev’s sense derivatives entering equation).

The most up-to-date version of this collection of homework exercises can always be found at 1. Find the general solution for the following first-order partial differential equation. 3u x + 5u y − xyu = 0 2. Find the general solution for the following first-order partial differential equation. u x − u y + yu = 0 3. Find the general solution for the following first-order partial differential equa...

this paper presents the jeffery hamel flow of a non-newtonian fluid namely casson fluid. suitable similarity transform is applied to reduce governing nonlinear partial differential equations to a much simpler ordinary differential equation. variation of parameters method (vpm) is then employed to solve resulting equation. same problem is solved numerical by using runge-kutta order 4 method. a c...

This paper presents the use of an iteration method to solve the identifiability problem for a class of discretized linear partial differential algebraic equations. This technique consists in replacing the partial derivatives in the PDAE by differences and analyzing the difference algebraic equations obtained. For that, the theory of discrete singular systems, which involves Drazin inverse matri...

We consider the 2-dimensional quasi-geostrophic equation with supercritical dissipation and dispersive forcing in the whole space. When the dispersive amplitude parameter is large enough, we prove the global well-posedness of strong solution to the equation with large initial data. We also show the strong convergence result as the amplitude parameter goes to ∞. Both results rely on the Strichar...

In this article it is shown how tool vibrations of elastic joint robots can be reduced significantly by feedforward control based on inverse dynamics models. The key ideas are (a) to use available algorithms for differential-algebraic equation systems to derive inverse plant models automatically and reliably, (b) to automatically construct the high-order differentiability of the inverse plant m...

friction is a nonlinear phenomenon which has destructive effects on performance of control systems. to obviate these effects, friction compensation is an effectual solution. in this paper, an adaptive technique is proposed in order to eliminate limit cycles as one of the undesired behaviors due to presence of friction in control systems which happen frequently. the proposed approach works for n...