Weak convergence theorems of three iterative methods for strictly pseudocontractive mappings of Browder-Petryshyn type.
Multi-point boundary value problems for higher order differential equations.
Existence criteria for singular boundary value problems with -Laplacian operators.
Dynamical instability of symmetric vortices.
Using the Maxwell-Higgs model, we prove that linearly unstable symmetric vortices in the Ginzburg-Landau theory are dynamically unstable in the H1 norm (which is the natural norm for the problem). In this work we study the dynamic instability of the radial solutions of the Ginzburg-Landau equations in R2 (...)
Nonlinear instability of double-humped equilibria
On the spectral instability of parallel shear flows
This short note is to announce our recent results [2,3] which provide a complete mathematical proof of the viscous destabilization phenomenon, pointed out by Heisenberg (1924), C.C. Lin and Tollmien (1940s), among other prominent physicists. Precisely, we construct growing modes of the linearized Navier-Stokes equations about general stationary shear flows in a bounded channel (channel flows) or on a half-space (boundary layers), for sufficiently large Reynolds number . Such an instability is linked...
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