105 research outputs found

    Global solvability and blow up for the convective Cahn-Hilliard equations with concave potentials

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    We study initial boundary value problems for the convective Cahn-Hilliard equation \Dt u +\px^4u +u\px u+\px^2(|u|^pu)=0. It is well-known that without the convective term, the solutions of this equation may blow up in finite time for any p>0p>0. In contrast to that, we show that the presence of the convective term u\px u in the Cahn-Hilliard equation prevents blow up at least for 0<p<490<p<\frac49. We also show that the blowing up solutions still exist if pp is large enough (p2p\ge2). The related equations like Kolmogorov-Sivashinsky-Spiegel equation, sixth order convective Cahn-Hilliard equation, are also considered

    Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent

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    In this paper the long time behaviour of the solutions of 3-D strongly damped wave equation is studied. It is shown that the semigroup generated by this equation possesses a global attractor in H_{0}^{1}(\Omega)\times L_{2}(\Omega) and then it is proved that this global attractor is a bounded subset of H^{2}(\Omega)\times H^{2}(\Omega) and also a global attractor in H^{2}(\Omega)\cap H_{0}^{1}(\Omega)\times H_{0}^{1}(\Omega)

    Delta-Function Potential with a Complex Coupling

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    We explore the Hamiltonian operator H=-d^2/dx^2 + z \delta(x) where x is real, \delta(x) is the Dirac delta function, and z is an arbitrary complex coupling constant. For a purely imaginary z, H has a (real) spectral singularity at E=-z^2/4. For \Re(z)<0, H has an eigenvalue at E=-z^2/4. For the case that \Re(z)>0, H has a real, positive, continuous spectrum that is free from spectral singularities. For this latter case, we construct an associated biorthonormal system and use it to perform a perturbative calculation of a positive-definite inner product that renders H self-adjoint. This allows us to address the intriguing question of the nonlocal aspects of the equivalent Hermitian Hamiltonian for the system. In particular, we compute the energy expectation values for various Gaussian wave packets to show that the non-Hermiticity effect diminishes rapidly outside an effective interaction region.Comment: Published version, 14 pages, 2 figure


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    The authors describe their first experience in using bipolar transurethral resection for a urinary bladder tumor. The obvious advantage of thistechnique over others suggests that in the immediate future the bipolar technology will serve as the gold standard instead of monopolar one.Опыт использования биполярной трансуретральной резекции в лечении поверхностных опухолей мочевого пузыр

    Phragmén-Lindelöe type theorems for two nonlinear problems in mechanics

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