Geodesic
Extinction of Solutions of Parabolic Equations with Variable Anisotropic Nonlinearities
Informatics and Automation, Differential equations and dynamical systems, Tome 261 (2008), pp. 16-25

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We study the Dirichlet problem for a class of nonlinear parabolic equations with nonstandard anisotropic growth conditions that generalize the evolutional $p(x,t)$-Laplacian. We study the property of extinction of solutions in finite time. In particular, we show that the extinction may take place even in the borderline case when the equation becomes linear as $t\to\infty$. 
@article{TRSPY_2008_261_a1,
     author = {S. N. Antontsev and S. I. Shmarev},
     title = {Extinction of {Solutions} of {Parabolic} {Equations} with {Variable} {Anisotropic} {Nonlinearities}},
     journal = {Informatics and Automation},
     pages = {16--25},
     publisher = {mathdoc},
     volume = {261},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2008_261_a1/}
}
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S. N. Antontsev; S. I. Shmarev. Extinction of Solutions of Parabolic Equations with Variable Anisotropic Nonlinearities. Informatics and Automation, Differential equations and dynamical systems, Tome 261 (2008), pp. 16-25. http://geodesic.mathdoc.fr/item/TRSPY_2008_261_a1/