| 1. |
- Basarab-Horwath, Peter, et al.
(author)
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Classifying evolution equations
- 2001
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In: Nonlinear Analysis. - 0362-546X .- 1873-5215. ; 47:8, s. 5135-5144
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Journal article (peer-reviewed)abstract
- A Lie point symmetry classification of evolution equations in 1+1 time-space dimensions was presented. A combination of the standard Lie algorithm for point symmetry and the equivalence group of the given type of equation was used for the classification. For each canonical evolution the maximal symmetry algebra was calculated and related theorems were proved.
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| 2. |
- Cheng, Yuanji
(author)
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Multiple solutions for prescribed boundary value problem
- 2002
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In: Nonlinear Analysis. - : Elsevier Science Ltd.. - 0362-546X .- 1873-5215. ; 51:3, s. 537-552
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Journal article (peer-reviewed)abstract
- We, in this paper, consider the semilinear elliptic boundary value problem - ∆u = f(x, u) in Ω and u = g on ∂Ω and the corresponding Bolza problem x'' + ∂V(t, x) =0, x(0)= x0, x(T)= x1, where Ω is a bounded open subset in R^n with C² boundary and g is a given continuous function on the boundary of Ω; and T is the given traveling time, x0,x1 are two fixed points in the state space Rn. Under certain conditions on f and V, we show that the above problems have infinitely many solutions
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| 3. |
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| 4. |
- Euler, Marianna, et al.
(author)
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n-Dimensional real wave equations and the D’Alembert-Hamilton system
- 2001
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In: Nonlinear Analysis. - 0362-546X .- 1873-5215. ; 47:8, s. 5125-5133
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Journal article (peer-reviewed)abstract
- We reduce the nonlinear wave equation □nu = αF[exp(βu)] to ordinary differential equtions and construct exact solutions, by the use of a compatible d'Alembert-Hamilton system. The solutions of these ordinary differential equations, together with the solutions of the corresponding d'Alembert-Hamilton equations, provide a rich class of exact solutions of the multidimensional wave equations. The wave equations are studied in n-dimensional Minkowski space.
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| 5. |
- Euler, Norbert, et al.
(author)
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On discrete velocity Boltzmann equations and the Painlevé analysis
- 2001
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In: Nonlinear Analysis. - 0362-546X .- 1873-5215. ; 47:2, s. 1407-1412
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Journal article (peer-reviewed)abstract
- The multidimensional Bateman equation is investigated to construct explicit solutions of two discrete velocity Boltzmann equations. The Painleve expansion and the general implicit solution are used to construct the solutions in (1 + 1) and (1 + 2) dimensions, respectively. Both these systems of partial differential equations do not pass the Painleve test for integrability.
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| 6. |
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| 7. |
- Lundström, Niklas L P, 1980-
(author)
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Estimates for p-harmonic functions vanishing on a flat
- 2011
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In: Nonlinear Analysis. - : Elsevier. - 0362-546X .- 1873-5215. ; 74:18, s. 6852-6860
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Journal article (peer-reviewed)abstract
- We study p-harmonic functions in a domain ΩCRn near an m-dimensional plane (an m-flat) Λm, where 0≤m≤n−1. In particular, let u be a positive p-harmonic function, with n<p≤∞, vanishing on a portion of Λm, and suppose that β=(p−n+m)/(p−1), with β=1 if p=∞. We prove, using certain barrier functions, that u ≈ d (x.Λm)8 near Λm.The lower bound holds also in the range n−m<p≤∞. Moreover, u∈C0,β near Λm and β is the optimal Hölder exponent of u.
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| 8. |
- Aiki, Toyohiko, et al.
(author)
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Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry’s law and time-dependent Dirichlet data
- 2013
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In: Nonlinear Analysis. - : Elsevier. - 0362-546X .- 1873-5215. ; 93, s. 3-14
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Journal article (peer-reviewed)abstract
- We study the large-time behavior of the free boundary position capturing the one-dimensional motion of the carbonation reaction front in concrete-based materials. We extend here our rigorous justification of the t-behavior of reaction penetration depths by including nonlinear effects due to deviations from the classical Henry's law and time-dependent Dirichlet data.
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| 9. |
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| 10. |
- Argaez, C., et al.
(author)
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Solutions to quasi-relativistic multi-configurative Hartree-Fock equations in quantum chemistry
- 2012
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In: Nonlinear Analysis. - : Elsevier BV. - 0362-546X .- 1873-5215. ; 75:1, s. 384-404
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Journal article (peer-reviewed)abstract
- We establish the existence of infinitely many distinct solutions to the multi-configurative Hartree-Fock type equations for N-electron Coulomb systems with quasi-relativistic kinetic energy root-alpha(-2)Delta(xn) + alpha(-4) - alpha(-2) for the nth electron. Finitely many of the solutions are interpreted as excited states of the molecule. Moreover, we prove the existence of a ground state. The results are valid under the hypotheses that the total charge Z(tot) of K nuclei is greater than N - 1 and that Z(tot) is smaller than a critical charge Z(c). The proofs are based on a new application of the Lions-Fang-Ghoussoub critical point approach to nonminimal solutions on a complete analytic Hilbert-Riemann manifold, in combination with density operator techniques. (C) 2011 Elsevier Ltd. All rights reserved.
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