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A generalization of the maximum principle to nonlinear parabolic systems

100%
Portnyagin D.
Annales Polonici Mathematici
|
2003
|
tom 81
|
nr 3
217-236
EN
A generalization of the well-known weak maximum principle is established for a class of quasilinear strongly coupled parabolic systems with leading terms of p-Laplacian type.
2
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Estimates of weak solutions to nondiagonal quasilinear parabolic systems

100%
Portnyagin D.
Annales Polonici Mathematici
|
2005
|
tom 85
|
nr 1
55-75
EN
$L^{∞}$-estimates of weak solutions are established for a quasilinear non-diagonal parabolic system with a special structure whose leading terms are modelled by p-Laplacians. A generalization of the weak maximum principle to systems of equations is employed.
3
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Full regularity of bounded solutions to nondiagonal parabolic systems of two equations

100%
Portnyagin D.
Applicationes Mathematicae
|
2008
|
tom 35
|
nr 1
69-79
EN
Hölder continuity and, basing on this, full regularity and global existence of weak solutions is studied for a general nondiagonal parabolic system of nonlinear differential equations with the matrix of coefficients satisfying special structure conditions and depending on the unknowns. A technique based on estimating a certain function of unknowns is employed to this end.
4
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Hölder continuity of weak solutions to nondiagonal singular parabolic systems of three equations

100%
Portnyagin D.
Annales Polonici Mathematici
|
2006
|
tom 88
|
nr 3
205-227
EN
Hölder continuity of weak solutions is studied for a nondiagonal parabolic system of singular quasilinear differential equations with matrix of coefficients satisfying special structure conditions. A technique based on estimating linear combinations of the unknowns is employed.
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