July  1997, 3(3): 305-316. doi: 10.3934/dcds.1997.3.305

Semilinear parabolic equations with distributions as initial data

1. 

C.M.L.A., U.R.A. 1611, E.N.S. de Cachan, 61 Av. du Président Wilson, 94235 Cachan Cedex, France

Received  October 1996 Published  April 1997

We study the local Cauchy problem for the semilinear parabolic equations

$\partial _t U-\Delta U=P(D)F(U), \quad (t,x) \in [0,T[ \times \mathbb{R}^n $

with initial data in Sobolev spaces of fractional order $H^s_p(\mathbb{R}^n)$. The techniques that we use allow us to consider measures but also distributions as initial data ($s<0$). We also prove some smoothing effects and $L^q([0,T[,L^p)$ estimates for the solutions of such equations.

Citation: Francis Ribaud. Semilinear parabolic equations with distributions as initial data. Discrete & Continuous Dynamical Systems - A, 1997, 3 (3) : 305-316. doi: 10.3934/dcds.1997.3.305
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