Results 11 to 20 of about 296 (72)
The Poisson equation in homogeneous Sobolev spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 36, Page 1909-1921, 2004., 2004 We consider Poisson′s equation in an n‐dimensional exterior domain G(n ≥ 2) with a sufficiently smooth boundary. We prove that for external forces and boundary values given in certain Lq(G)‐spaces there exists a solution in the homogeneous Sobolev space S2,q(G), containing functions being local in Lq(G) and having second‐order derivatives in Lq(G ...
Tatiana Samrowski, Werner Varnhorn
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Generalized Cahn‐Hilliard equations based on a microforce balance
Journal of Applied Mathematics, Volume 2003, Issue 4, Page 165-185, 2003., 2003 We present some models of Cahn‐Hilliard equations based on a microforce balance proposed by M. Gurtin. We then study the existence and uniqueness of solutions.
Alain Miranville
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Positive solutions of higher order quasilinear elliptic equations
Abstract and Applied Analysis, Volume 7, Issue 8, Page 423-452, 2002., 2002 The higher order quasilinear elliptic equation −Δ(Δp(Δu)) = f(x, u) subject to Dirichlet boundary conditions may have unique and regular positive solution. If the domain is a ball, we obtain a priori estimate to the radial solutions via blowup. Extensions to systems and general domains are also presented. The basic ingredients are the maximum principle,
Marcelo Montenegro
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Abstract and Applied Analysis, Volume 7, Issue 10, Page 547-561, 2002., 2002 We study the location of the peaks of solution for the critical growth problem −ε 2Δu+u=f(u)+u 2*−1, u > 0 in Ω, u = 0 on ∂Ω, where Ω is a bounded domain; 2* = 2N/(N − 2), N ≥ 3, is the critical Sobolev exponent and f has a behavior like up, 1 < p < 2* − 1.
Marco A. S. Souto
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Uniqueness of weak solution for nonlinear elliptic equations in divergence form
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 5, Page 313-318, 2000., 2000 We study the uniqueness of weak solutions for quasilinear elliptic equations in divergence form. Some counterexamples are given to show that our uniqueness result cannot be improved in the general case.
Xu Zhang
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A Picard‐Maclaurin theorem for initial value PDEs
Abstract and Applied Analysis, Volume 5, Issue 1, Page 47-63, 2000., 2000 In 1988, Parker and Sochacki announced a theorem which proved that the Picard iteration, properly modified, generates the Taylor series solution to any ordinary differential equation (ODE) on ℜn with a polynomial generator. In this paper, we present an analogous theorem for partial differential equations (PDEs) with polynomial generators and analytic ...
G. Edgar Parker, James S. Sochacki
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Oscillatory and periodic solutions to a diffusion equation of neutral type
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 2, Page 313-348, 1999., 1999 We examine a PDE with piecewise constant time delay. The equation is of neutral type since it contains the derivative ut at different values of the t‐argument. Furthermore, the argument deviation changes its sign within intervals of unit length, so that the given PDE is alternately of retarded and advanced type.
Joseph Wiener, William Heller
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Well-posedness and long-time behavior for a nonstandard viscous Cahn-Hilliard system [PDF]
, 2011 We study a diffusion model of phase field type, consisting of a system of two partial differential equations encoding the balances of microforces and microenergy; the two unknowns are the order parameter and the chemical potential.
Colli, Pierluigi +3 more
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Nonlinear functional integrodifferential equations in Hilbert space
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 4, Page 847-854, 1999., 1999 Let X be a Hilbert space and let Ω ⊂ Rn be a bounded domain with smooth boundary ∂Ω. We establish the existence and norm estimation of solutions for the parabolic partial functional integro‐differential equation in X by using the fundamental solution.
J. Y. Park, S. Y. Lee, M. J. Lee
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Uniqueness and comparison principles for semilinear equations and inequalities in Carnot groups
Advances in Nonlinear Analysis, 2018 Variants of the Kato inequality are proved for distributional solutions of semilinear equations and inequalities on Carnot groups. Various applications to uniqueness, comparison of solutions and Liouville theorems are presented.
D’Ambrosio Lorenzo, Mitidieri Enzo
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