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We construct finite time blow-up solutions to the 3-dimensional harmonic map flow into the sphere S2, ut = ∆u + |∇u|2u in Ω × (0, T) u = ub on ∂Ω × (0, T) u(·, 0) = u0 in Ω, with u(x, t)...
We consider a family of evolution equations that generalize the Peierls-Nabarro model for crystal dislocations. They can be seen as semilinear parabolic reaction-diffusion equations in which the diffusion is regulated by a...
We consider a family of evolution equations that generalize the Peierls-Nabarro model for crystal dislocations. They can be seen as semilinear parabolic reaction-diffusion equations in which the diffusion is regulated by a...
We construct finite time blow-up solutions to the 3-dimensional harmonic map flow into the sphere S2, ut = ∆u + |∇u|2u in Ω × (0, T) u = ub on ∂Ω × (0, T) u(·, 0) = u0 in Ω, with u(x, t)...
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