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Singular Potential (singular + potential)
Selected AbstractsBlow-up analysis, existence and qualitative properties of solutions for the two-dimensional Emden,Fowler equation with singular potentialMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 18 2007Daniele Bartolucci Abstract Motivated by the study of a two-dimensional point vortex model, we analyse the following Emden,Fowler type problem with singular potential: where V(x) = K(x)/|x|2, with ,,(0, 1), 0 Well-posedness and long time behavior of a parabolic-hyperbolic phase-field system with singular potentialsMATHEMATISCHE NACHRICHTEN, Issue 13-14 2007Maurizio Grasselli Abstract In this article, we study the long time behavior of a parabolic-hyperbolic system arising from the theory of phase transitions. This system consists of a parabolic equation governing the (relative) temperature which is nonlinearly coupled with a weakly damped semilinear hyperbolic equation ruling the evolution of the order parameter. The latter is a singular perturbation through an inertial term of the parabolic Allen,Cahn equation and it is characterized by the presence of a singular potential, e.g., of logarithmic type, instead of the classical double-well potential. We first prove the existence and uniqueness of strong solutions when the inertial coefficient , is small enough. Then, we construct a robust family of exponential attractors (as , goes to 0). (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Studies on some singular potentials in quantum mechanicsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 6 2005Amlan K. RoyArticle first published online: 10 MAY 200 Abstract A simple methodology is suggested for the efficient calculation of certain central potentials having singularities. The generalized pseudospectral method used in this work facilitates nonuniform and optimal spatial discretization. Applications have been made to calculate the energies, densities, and expectation values for two singular potentials of physical interest, viz., (i) the harmonic potential plus inverse quartic and sextic perturbation and (ii) the Coulomb potential with a linear and quadratic term for a broad range of parameters. The first 10 states belonging to a maximum of ,, = 8 and 5 for (i) and (ii) have been computed with good accuracy and compared with the most accurate available literature data. The calculated results are in excellent agreement, especially in light of the difficulties encountered in these potentials. Some new states are reported here for the first time. This offers a general and efficient scheme for calculating these and other similar potentials of physical and mathematical interest in quantum mechanics accurately. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] Well-posedness and long time behavior of a parabolic-hyperbolic phase-field system with singular potentialsMATHEMATISCHE NACHRICHTEN, Issue 13-14 2007Maurizio Grasselli Abstract In this article, we study the long time behavior of a parabolic-hyperbolic system arising from the theory of phase transitions. This system consists of a parabolic equation governing the (relative) temperature which is nonlinearly coupled with a weakly damped semilinear hyperbolic equation ruling the evolution of the order parameter. The latter is a singular perturbation through an inertial term of the parabolic Allen,Cahn equation and it is characterized by the presence of a singular potential, e.g., of logarithmic type, instead of the classical double-well potential. We first prove the existence and uniqueness of strong solutions when the inertial coefficient , is small enough. Then, we construct a robust family of exponential attractors (as , goes to 0). (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]
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