Results 11 to 20 of about 1,290,485 (220)
Topological Derivatives for Semilinear Elliptic Equations [PDF]
International Journal of Applied Mathematics and Computer Science, 2009 Topological Derivatives for Semilinear Elliptic EquationsThe form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in theL∞norm are obtained.
Mohamed Iguernane +4 more
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Some maximum principles in semilinear elliptic equations [PDF]
Proceedings of the American Mathematical Society, 1986 We develop maximum principles for functions defined on the solutions to a class of semilinear, second order, uniformly elliptic partial differential equations. These principles are related to recent theorems of Protter and Protter and Weinberger and to a technique initiated by Payne for the determination of gradient bounds on the solution of the ...
Philip W. Schaefer
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A singularly perturbed semilinear reaction-diffusion problem in a polygonal domain [PDF]
, 2010 The semilinear reaction-di®usion equation ¡"24u+b(x; u) = 0 with Dirichlet bound-ary conditions is considered in a convex polygonal domain. The singular perturbation parameter ε is arbitrarily small, and the “reduced equation” b(x, u0 (x)) = 0 may have ...
Kellogg, R. Bruce, Kopteva, Natalia
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Maximum norm a posteriori error estimation for parabolic problems using elliptic reconstructions [PDF]
, 2013 A semilinear second-order parabolic equation is considered in a regular and a singularly perturbed regime. For this equation, we give computable a posteriori error estimates in the maximum norm.
Linss, Torsten, Kopteva, Natalia
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On a Model Semilinear Elliptic Equation in the Plane [PDF]
Journal of Mathematical Sciences, 2016 This paper deals with the blow-up problem for a model semilinear equation of the type \[ \text{div}(A(z)\nabla u)= e^u \] in a simply connected domain \(\Omega\subset \mathbb{C}^1\). \(A(z)\) is a \(2\times 2\) symmetric uniformly elliptic matrix with measurable entries and \(\text{det\,}A=1\).
Gutlyanskii, V.Y. +2 more
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Solutions of Semilinear Elliptic Equations in Tubes [PDF]
Journal of Geometric Analysis, 2012 Given a smooth compact k-dimensional manifold Λembedded in $\mathbb {R}^m$, with m\geq 2 and 1\leq k\leq m-1, and given ε>0, we define B_ε(Λ) to be the geodesic tubular neighborhood of radius εabout Λ. In this paper, we construct positive solutions of the semilinear elliptic equation Δu + u^p = 0 in B_ε(Λ) with u = 0 on \partial B_ε(Λ), when the ...
Frank Pacard +2 more
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Multiple solutions for a semilinear elliptic equation [PDF]
Transactions of the American Mathematical Society, 1995 Let Ω \Omega be a bounded, smooth ...
del Pino, Manuel A., Felmer, Patricio L.
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A Concentration Phenomenon for Semilinear Elliptic Equations [PDF]
Archive for Rational Mechanics and Analysis, 2012 For a domain $Ω\subset\dR^N$ we consider the equation $ -Δu + V(x)u = Q_n(x)\abs{u}^{p-2}u$ with zero Dirichlet boundary conditions and $p\in(2,2^*)$. Here $V\ge 0$ and $Q_n$ are bounded functions that are positive in a region contained in $Ω$ and negative outside, and such that the sets $\{Q_n>0\}$ shrink to a point $x_0\inΩ$ as $n\to\infty$.
Ackermann, Nils, Szulkin, Andrzej
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The structure of solutions of a semilinear elliptic equation [PDF]
Transactions of the American Mathematical Society, 1992 We give a complete classification of solutions of the elliptic equation Δ u
Cheng, Kuo-Shung, Lin, Tai-Chia
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Isolated boundary singularities of semilinear elliptic equations [PDF]
Calculus of Variations and Partial Differential Equations, 2010 Given a smooth domain $Ω\subset\RR^N$ such that $0 \in \partialΩ$ and given a nonnegative smooth function $ζ$ on $\partialΩ$, we study the behavior near 0 of positive solutions of $-Δu=u^q$ in $Ω$ such that $u = ζ$ on $\partialΩ\setminus\{0\}$. We prove that if $\frac{N+1}{N-1} < q < \frac{N+2}{N-2}$, then $u(x)\leq C \abs{x}^{-\frac{2}{q-1 ...
Bidaut-Veron, Marie-Françoise +2 more
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