Lingeshwaran Shangerganesh, Arumugam Gurusamy, Krishnan Balachandran (2017)
Communications in Mathematics
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In this work, we study the existence and uniqueness of weak solutions of fourth-order degenerate parabolic equation with variable exponent using the difference and variation methods.
D. G. Aronson (1968)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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D. G. Aronson (1965)
Annales Polonici Mathematici
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Tuomo Kuusi (2008)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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In this work we prove both local and global Harnack estimates for weak supersolutions to second order nonlinear degenerate parabolic partial differential equations in divergence form. We reduce the proof to an analysis of so-called hot and cold alternatives, and use the expansion of positivity together with a parabolic type of covering argument. Our proof uses only the properties of weak supersolutions. In particular, no comparison to weak solutions is needed.
Ivanov, Alexander V.
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Zbigniew Slodkowski, Giuseppe Tomassini (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Bjorn E. J. Dahlberg, Carlos E. Kenig (1988)
Revista Matemática Iberoamericana
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The purpose of this work is to study the class of non-negative continuous weak solutions of the non-linear evolution equation ∂u/∂t = ∆φ(u), x ∈ Rn, 0 < t < T ≤ +∞.