Differential and Integral Equations

A heat equation with a nonlinear nonlocal term in time and singular initial data

M. Loayza and I. Quinteiro

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Abstract

We consider the general semilinear parabolic equation $u_t-\Delta u=\int_0^t k(t,s)|u|^{p-1}u(s)ds$ in $(0,T)\times \mathbb{R}^N$ with $p > 1$. The function $k:\{(t,s); s < t\} \to \mathbb{R}$ is continuous and verifies a scaling property. We prove the existence and non existence results for initial data in the space $L^r(\mathbb{R}^N)$ with $1\leq r < \infty$.

Article information

Source
Differential Integral Equations, Volume 27, Number 5/6 (2014), 447-460.

Dates
First available in Project Euclid: 3 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.die/1396558091

Mathematical Reviews number (MathSciNet)
MR3189527

Zentralblatt MATH identifier
1340.35164

Subjects
Primary: 35K58: Semilinear parabolic equations 35D30: Weak solutions 35R05: Partial differential equations with discontinuous coefficients or data

Citation

Quinteiro, I.; Loayza, M. A heat equation with a nonlinear nonlocal term in time and singular initial data. Differential Integral Equations 27 (2014), no. 5/6, 447--460. https://projecteuclid.org/euclid.die/1396558091


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