Global ETD Search
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Showing 1 to 5 of 5 for “"Blow-up solutions"”.
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An Adaptive Method for Calculating Blow-Up Solutions
… of the independent variable referred to as "blow-up." The attempt to find the blow-up time analytically is most often impossible, thus requiring a numerical determination of the value. The numerical methods often use <em>a priori</em> knowledge of the blow-up solution such as monotonicity or …
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On long time dynamic and singularity formation of NLS
… first part, we give a construction of log-log blow up solutions which blow up at m prescribed points simultaneously. In the second part, we show weak convergence to ground state for certain radial blow up solutions to NLS at well chosen time sequence. We also include a lecture note on …
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Nonlinear Methods in the Study of Singular Partial Differential Equations
… the knowledge of qualitative properties of the solutions to equations of the form &Delta u= &fnof(x,u) where &Omega is a smooth domain in R^N (bounded or possibly unbounded) with compact (possibly empty) boundary &part&Omega. A non-negative solution of the above equation subject to the singular …
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On the discrete nonlinear Schrödinger equation with PT-Symmetry
… nonlinear Schrödinger equation (known as Ablowitz-Ladik equation) with parity-time symmetry proposed in Ablowitz and Musslimani’s paper. This includes the eigenfunctions (Jost solutions) of the associated Lax pair, the scattering data and the fundamental analytic solutions. In addition, we …
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Modeling Temperature Dependence in Marangoni-driven Thin Films
… through numerical computation of solutions, qualitative analysis,</p><p>and asymptotic analysis. A thorough comparison is made between the</p><p>behavior of solutions to the temperature-independent and</p><p>temperature-dependent models. It is shown that using</p><p>localized …