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Oscillatory Doubly Diffusive Convection In A Finite Container, Adam S. Landsberg, Edgar Knobloch
Oscillatory Doubly Diffusive Convection In A Finite Container, Adam S. Landsberg, Edgar Knobloch
WM Keck Science Faculty Papers
Oscillatory doubly diffusive convection in a large aspect ratio Hele-Shaw cell is considered. The partial differential equations are reduced via center-unstable manifold reduction to the normal form equations describing the interaction of even and odd parity standing waves near onset. These equations take the form of the equations for a Hopf bifurcation with approximate D4 symmetry, verifying the conclusions of the preceding paper [A.S. Landsberg and E. Knobloch, Phys. Rev. E 53, 3579 (1996)]. In particular, the amplitude equations differ in the limit of large aspect ratios from the usual Ginzburg-Landau description in having additional nonlinear terms with O(1) coefficients. …
Radial Solutions To A Dirichlet Problem Involving Critical Exponents When N=6, Alfonso Castro, Alexandra Kurepa
Radial Solutions To A Dirichlet Problem Involving Critical Exponents When N=6, Alfonso Castro, Alexandra Kurepa
All HMC Faculty Publications and Research
In this paper we show that, for each λ>0, the set of radially symmetric solutions to the boundary value problem
-Δu(x) = λu(x) + u(x)|u(x)|, x ε B := {x ε R6:|x|<1},
u(x) = 0, x ε ∂B
is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity.