Differential and Integral Equations

Global Sobolev Solutions of Quasilinear Parabolic Equations

Kevin McLeod and Albert Milani

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We prove that the quasilinear parabolic initial-boundary value problem (1.1) below is globally well-posed in a class of high order Sobolev solutions.

Article information

Differential Integral Equations, Volume 11, Number 3 (1998), 521-550.

First available in Project Euclid: 30 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B45: A priori estimates 35B60: Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx] 35B65: Smoothness and regularity of solutions 35K55: Nonlinear parabolic equations 35K60: Nonlinear initial value problems for linear parabolic equations


McLeod, Kevin; Milani, Albert. Global Sobolev Solutions of Quasilinear Parabolic Equations. Differential Integral Equations 11 (1998), no. 3, 521--550. https://projecteuclid.org/euclid.die/1367341066

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