17 research outputs found
On some sufficient conditions for the blow-up solutions of the nonlinear Ginzburg-Landau-Schrödinger evolution equation
No full textInvestigation of the
blow-up solutions of the problem in finite time of the first
mixed-value problem with a homogeneous boundary condition on a
bounded domain of n-dimensional Euclidean space for a class of
nonlinear Ginzburg-Landau-Schrödinger evolution equation is
continued. New simple sufficient conditions have been obtained
for a wide class of initial data under which collapse happens for
the given new values of parameters
Collapse Rate of Solutions of the Cauchy Problem for the Nonlinear Schrödinger Equation
No full textUpper and lower bounds for the optimal constant in the extended Sobolev inequality. Derivation and numerical results
No full textWe prove and give numerical results for two lower bounds and eleven upper bounds to the optimal constant k0 = k0(n,α) in the inequality â„uâ„2n/(n-2α) †k0 â„âuâ„α2 â„uâ„1-α 2, u â H1(ân), for n = 1, 0 < α †1/2, and n â„ 2, 0 < α < 1. This constant k0 is the reciprocal of the infimum λn,α for u â H1(ân) of the functional În,α = â„âuâ„α2 â„uâ„1-α 2/â„uâ„2n/(n-2α), u â H1(ân), where for n = 1, 0 < α †1/2, and for n â„ 2, 0 < α < 1. The lowest point in the point spectrum of the Schrödinger operator Ï = -Î+q on ân with the real-valued potential q can be expressed in λn,α for all q _ = max(0,-q) â Lp(ân), for n = 1, 1 †p < â, and n â„ 2, n/2 < p < â, and the norm â„q _ â„p.Water Resource
Remarks on the Gross-Sobolev, Hirschman, and Pauli-Heisenberg-Weyl fundamental inequalities and the entropy inequality
No full text
