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Remarks on the strong maximum principle for viscosity solutions to fully nonlinear parabolic equations
On the Cauchy problem for a coupled system of KdV equations
1. | IMPA, Estrada Dona Castorina 110, Rio de Janeiro, 22460-320, Brazil |
2. | Instituto de Matemática Pura e Aplicada, 22460-320, Rio de Janeiro, Brazil |
$u_{t}+u_{x x x}+a_3 v_{x x x}+u u_{x}+a_1 v v_{x}+a_2(uv)_x =0,$
$b_1 v_{t}+v_{x x x}+b_2 a_3 u_{x x x}+v v_{x}+b_2 a_2 u u_{x}+b_2 a_1(uv)_x=0.$
Using recent methods, we prove a sharp local result in Sobolev spaces. We also prove global result under some conditions on the coefficients.
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