Uniqueness/nonuniqueness for nonnegative solutions of a class of second-order parabolic equations

An abstract parabolic equation with sectorial operator and continuous nonlinearity is studied in this paper. In particular, the asymptotic behavior of solutions is described within the framework of the theory of global attractors. Examples included in the final part of the paper illustrate the presented ideas.

Sufficient conditions for nonexistence of gradient blow-up for nonlinear parabolic equations.

Tersenov, Aris S. (2007)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Vanishing of solutions of diffusion equation with convection and absorption.

Gladkov, Alexander, Prokhozhy, Sergey (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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