Geodesic
Local and Global Estimates of the Solutions of the Cauchy Problem for Quasilinear Parabolic Equations with a Nonlinear Operator of Baouendi--Grushin Type
Matematičeskie zametki, Tome 85 (2009) no. 3, pp. 395-407

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In this paper, the qualitative properties of the solutions of the Cauchy problem for degenerate parabolic equations with a nonlinear operator of Baouendi–Grushin type are studied. Sharp local and global (with respect to the spatial and temporal variables) estimates of the solution are obtained. The property of the finiteness of the support of the solution is established.
Keywords: quasilinear parabolic equation, nonlinear operator, Cauchy problem, Carnot–Carathéodory space, Young's inequality, maximum principle. 
@article{MZM_2009_85_3_a7,
     author = {V. A. Markasheva and A. F. Tedeev},
     title = {Local and {Global} {Estimates} of the {Solutions} of the {Cauchy} {Problem} for {Quasilinear} {Parabolic} {Equations} with a {Nonlinear} {Operator} of {Baouendi--Grushin} {Type}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {395--407},
     publisher = {mathdoc},
     volume = {85},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_3_a7/}
}
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V. A. Markasheva; A. F. Tedeev. Local and Global Estimates of the Solutions of the Cauchy Problem for Quasilinear Parabolic Equations with a Nonlinear Operator of Baouendi--Grushin Type. Matematičeskie zametki, Tome 85 (2009) no. 3, pp. 395-407. http://geodesic.mathdoc.fr/item/MZM_2009_85_3_a7/