| 1. |
- Akhmetkaliyeva, Raya D., et al.
(författare)
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Some new results concerning a class of third-order differential equations
- 2015
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Ingår i: Applicable Analysis. - : Taylor & Francis. - 0003-6811 .- 1563-504X. ; 94:2, s. 419-434
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Tidskriftsartikel (refereegranskat)abstract
- We consider the following third-order differential equation with unbounded coefficients:Some new existence and uniqueness results are proved, and precise estimates of the norms of the solutions are given. The obtained results may be regarded as a unification and extension of all other results of this type
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| 2. |
- Barkhudaryan, R., et al.
(författare)
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System of variational inequalities with interconnected obstacles
- 2020
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Ingår i: Applicable Analysis. - : Taylor & Francis. - 0003-6811 .- 1563-504X.
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Tidskriftsartikel (refereegranskat)abstract
- Our objective with this paper is to discuss multi-switching problems, arising as variational inequalities, that models decision under uncertainty. We prove general existence theory through monotone scheme and discuss iterative methods for numerical results. We also connect the recently developed models for asset bubbles (which is a non-local problem) to switching problems with two possible switching cases.
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| 3. |
- Beilina, Larisa, 1970
(författare)
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Adaptive Finite Element Method for a coefficient inverse problem for the Maxwell's system
- 2011
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Ingår i: Applicable Analysis. - : Informa UK Limited. - 0003-6811 .- 1563-504X. ; 90:10, s. 1461-1479
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Tidskriftsartikel (refereegranskat)abstract
- We consider a coefficient inverse problem for Maxwell's system in 3-D. The coefficient of interest is the dielectric permittivity function. Only backscattering single measurement data are used. The problem is formulated as an optimization problem. The key idea is to use the adaptive finite element method for the solution. Both analytical and numerical results are presented. Similar ideas for inverse problems for the complete time dependent Maxwell's system were not considered in the past.
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| 4. |
- Beilina, Larisa, 1970, et al.
(författare)
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Relaxation property for the adaptivity for ill-posed problems
- 2014
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Ingår i: Applicable Analysis. - : Informa UK Limited. - 0003-6811 .- 1563-504X. ; 93:2, s. 223-253
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Tidskriftsartikel (refereegranskat)abstract
- Adaptive finite element method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property is the central part of this paper. In terms of coefficient inverse problems with single measurement data, the authors consider the adaptivity as the second stage of a two-stage numerical procedure. The first stage delivers a good approximation of the exact coefficient without an advanced knowledge of a small neighborhood of that coefficient. This is a necessary element for the adaptivity to start iterations from. Numerical results for the two-stage procedure are presented for both computationally simulated and experimental data.
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| 5. |
- Douanla Yonta, Hermann, 1982, et al.
(författare)
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Homogenization of a nonlinear elliptic problem with large nonlinear potential
- 2012
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Ingår i: Applicable Analysis. - : Informa UK Limited. - 0003-6811 .- 1563-504X. ; 91:6, s. 1205-1218
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Tidskriftsartikel (refereegranskat)abstract
- Homogenization is studied for a nonlinear elliptic boundary-value problem with a large nonlinear potential. More specifically we are interested in the asymptotic behaviour of a sequence of p-Laplacians of the form -div(a(x/epsilon)vertical bar Du(epsilon vertical bar)(p-2)Du(epsilon)) + 1/epsilon V(x/epsilon)vertical bar u(epsilon)vertical bar(p-2)u(epsilon) = f. It is shown that, under a centring condition on the potential V, there exists a two-scale homogenized system with solution (u, u(1)) such that the sequence u(epsilon) of solutions converges weakly to u in W-1,W-p and the gradients D(x)u(epsilon) two-scale converges weakly to D(x)u+D(y)u(1) in L-p, respectively. We characterize the limit system explicitly by means of two-scale convergence and a new convergence result.
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| 6. |
- Fabricius, John, et al.
(författare)
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On pressure-driven Hele–Shaw flow of power-law fluids
- 2022
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Ingår i: Applicable Analysis. - : Taylor & Francis. - 0003-6811 .- 1563-504X. ; 101:14, s. 5107-5137
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Tidskriftsartikel (refereegranskat)abstract
- We analyze the asymptotic behavior of a non-Newtonian Stokes system, posed in a Hele–Shaw cell, i.e. a thin three-dimensional domain which is confined between two curved surfaces and contains a cylindrical obstacle. The fluid is assumed to be of power-law type defined by the exponent 1< p<∞. By letting the thickness of the domain tend to zero we obtain a generalized form of the Poiseuille law, i.e. the limit velocity is a nonlinear function of the limit pressure gradient. The flow is assumed to be driven by an external pressure which is applied as a normal stress along the lateral part of the boundary. On the remaining part of the boundary we impose a no-slip condition. The two-dimensional limit problem for the pressure is a generalized form of the p′-Laplace equation, 1/p+1/p'=1, with a coefficient called ‘flow factor’, which depends on the geometry as well as the power-law exponent. The boundary conditions are preserved in the limit as a Dirichlet condition for the pressure on the lateral boundary and as a Neumann condition for the pressure on the solid obstacle.
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| 7. |
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| 8. |
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| 9. |
- Iantchenko, Alexei
(författare)
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Resonance spectrum for one-dimensional layered media
- 2006
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Ingår i: Applicable Analysis. - : Informa UK Limited. - 0003-6811 .- 1563-504X. ; 85:11, s. 1383-1410
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Tidskriftsartikel (refereegranskat)abstract
- We consider the “weighted” operator Pk= - ∂x a(x)∂ x on the real line with a step-like coefficient which appears when propagation of waves through a finite slab of a periodic medium is studied. The medium is transparent at certain resonant frequencies which are related to the complex resonance spectrum of Pk. If the coefficient is periodic on a finite interval (locally periodic) with k identical cells, then the resonance spectrum of Pk has band structure. In the article, we study a transition to semi-infinite medium by taking the limit ∞ . The bands of resonances in the complex lower half plane are localized below the band spectrum of the corresponding periodic problem (k=∞) with k - 1 or k resonances in each band. We prove that as ∞ , the resonance spectrum converges to the real axis.
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| 10. |
- Jalilian, Yaghoub, et al.
(författare)
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Infinitely many solutions for semilinear elliptic problems with sign-changing weight functions :
- 2014
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Ingår i: Applicable Analysis. - : Informa UK Limited. - 0003-6811 .- 1563-504X. ; 93:4, s. 756-770
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study the elliptic problem\begin{equation*} \left\{\begin{array}{ll} -\Delta u+u = a(x)|u|^{p-2}u+b(x)|u|^{q-2}u,\\ u\in H^{1}(\mathbb{R}^{N}),\end{array}\right.\end{equation*}where $2^{*}$ is the critical Sobolev exponent, $2< p
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