Differential and Integral Equations

The Carleman inequality for linear parabolic equations in $L^q$-norm

V. Barbu

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The Carleman inequality for linear parabolic equations (see [5]) is extended to $L^q, 1\leq q\leq 2$ norm. Two applications pertaining maximum principle for the Bolza problem and stabilization of the semilinear heat equation are given.

Article information

Differential Integral Equations, Volume 15, Number 5 (2002), 513-525.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K20: Initial-boundary value problems for second-order parabolic equations
Secondary: 35B35: Stability 35B45: A priori estimates 35B50: Maximum principles 35K55: Nonlinear parabolic equations


Barbu, V. The Carleman inequality for linear parabolic equations in $L^q$-norm. Differential Integral Equations 15 (2002), no. 5, 513--525. https://projecteuclid.org/euclid.die/1356060828

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