# American Institute of Mathematical Sciences

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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