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math.AP2017
Well-posedness of a Debye type system endowed with a full wave equation
Arnaud Heibig
We prove well-posedness for a transport-diffusion problem coupled with a wave equation for the potential. We assume that the initial data are small. A bilinear form in the spirit o…
math.FA2017
A generalized Cauchy-Lipschitz theorem in low regularity spaces
Arnaud Heibig
We prove well-posedness for some abstract differential equations of the first order. Our result covers the usual case of Lipschitz composition operators. It also contains the case…