Advances in Differential Equations

Semilinear parabolic equations in $L^1(\Omega)$

Gabriella Di Blasio

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This paper studies existence, regularity and continuous dependence upon the data of solutions to parabolic semilinear problems of the form: $u'(t)=Au(t) +g[u(t)]$, $u(0)=u_0$. Here, $A:D(A)\to X$ generates an analytic semigroup on a Banach space $X$ and $g:D(g)\to X$. It is assumed that $D(g)$ contains a certain interpolation space of $X$ and $D(A)$; this will allow to treat parabolic partial semilinear problems in the cases where the nonlinear term depends also on the gradient of $u$.

Article information

Adv. Differential Equations, Volume 12, Number 12 (2007), 1393-1414.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations
Secondary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx] 35K20: Initial-boundary value problems for second-order parabolic equations 35K90: Abstract parabolic equations


Di Blasio, Gabriella. Semilinear parabolic equations in $L^1(\Omega)$. Adv. Differential Equations 12 (2007), no. 12, 1393--1414.

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