Center for Mathematical Modeling

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20032013

most citedNonlocal anisotropic dispersal with monostable nonlinearity

177 citations

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Showing 2013Show all

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math.AP2013★ 2 cited

A Monotonicity Formula and a Liouville-type Theorem for a Fourth Order Supercritical Problem

Juan Davila, Louis Dupaigne, Kelei Wang +1

We consider Liouville-type and partial regularity results for the nonlinear fourth-order problem $$ Δ^2 u=|u|^{p-1}u\ \{in} \ \R^n,$$ where $p > 1$ and $n \geq 1$ . We give a complete c…

math.AP2013★ 108 cited

Pulsating fronts for nonlocal dispersion and KPP nonlinearity

Jerome Coville, Juan Davila, Salome Martinez

In this paper we are interested in propagation phenomena for nonlocal reaction-diffusion equations of the type: $δ_{t} u = J \times u - u + f (x, u) t \in R^{+}, x \in R^{N}$ , where J is…

math.AP2013

A new critical curve for the Lane-Emden system

Wenjing Chen, Louis Dupaigne, Marius Ghergu

We study stable positive radially symmetric solutions for the Lane-Emden system $- Δ u = v^{p}$ in $R^{N}$ , $- Δ v = u^{q}$ in $R^{N}$ , where $p, q \geq 1$ . We obtain a new critical curve that opt…