Results 1 to 10 of about 1,054 (47)
A note on Serrin's overdetermined problem [PDF]
, 2014 We consider the solution of the torsion problem $-\Delta u=1$ in $\Omega$ and $u=0$ on $\partial \Omega$. Serrin's celebrated symmetry theorem states that, if the normal derivative $u_\nu$ is constant on $\partial \Omega$, then $\Omega$ must be a ball ...
Ciraolo, Giulio, Magnanini, Rolando
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Physiologically structured populations with diffusion and dynamic boundary conditions [PDF]
, 2011 We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. The model is equipped with generalized Wentzell-Robin (or dynamic) boundary conditions.
Farkas, J. Z., Hinow, P.
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On the instability of a nonlocal conservation law [PDF]
, 2011 We are interested in a nonlocal conservation law which describes the morphodynamics of sand dunes sheared by a fluid flow, recently proposed by Andrew C. Fowler. We prove that constant solutions of Fowler's equation are non-linearly unstable.
Bouharguane, Afaf
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Dynamics on resonant clusters for the quintic non linear Schr\"odinger equation [PDF]
, 2012 We construct solutions to the quintic nonlinear Schr\"odinger equation on the circle with initial conditions supported on arbitrarily many different resonant clusters.
Haus, Emanuele, Thomann, Laurent
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Size-structured populations: immigration, (bi)stability and the net growth rate [PDF]
, 2009 We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the linearised system is
A.S. Ackleh +23 more
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Critical Exponents of Semilinear Equations via the Feynman-Kac Formula [PDF]
, 2007 2000 Mathematics Subject Classification: 60H30, 35K55, 35K57 ...
Alfredo Lopez-Mimbela, Jose +1 more
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, 2014 We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity, this seems to
Chae, Dongho +2 more
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Stability and Instability of Solitary Wave Solutions of a Nonlinear Dispersive System of Benjamin-Bona-Mahony Type [PDF]
, 2003 2000 Mathematics Subject Classification: 35B35, 35B40, 35Q35, 76B25, 76E30.This paper concerns the orbital stability and instability of solitary waves of the system of coupling equations of Benjamin-Bona-Mahony type.
Hakkaev, Sevdzhan
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On a Cubic-Quintic Ginzburg-Landau Equation with Global Coupling [PDF]
, 2005 We study standing wave solutions in a Ginzburg-Landau equation which consists of a cubic-quintic equation stabilized by global coupling A_t= \Delta A +\mu A + c A^3 -A^5 -k A (\int_{R^n} A^2\,dx).
Wei, J, Winter, M
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Existence of stable solutions to $(-\Delta)^m u=e^u$ in $\mathbb{R}^N$ with $m \geq 3$ and $N > 2m$
, 2015 We consider the polyharmonic equation $(-\Delta)^m u=e^u$ in $\mathbb{R}^N$ with $m \geq 3$ and $N > 2m$. We prove the existence of many entire stable solutions.
Huang, Xia, Ye, Dong
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