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Existence and uniqueness of periodic solutions for a quasilinear parabolic problem
Badii, Maurizio
2000
Abstract
We are concerned with the existence and uniqueness of
the nonnegative periodic weak solution to a quasilinear parabolic
problem of degenerate type, which describes a mathematical model
in petroleum engineering. The existence of periodic solutions is
established by means of the Schauder fixed point Theorem applied
to the Poincaré map. Instead, the uniqueness of the periodic
solution is proved under the assumption that $b(\varphi^-1)$ is Hölder
continuous of order 1/2, adapting a technique utilized in the study
of nonlinear hyperbolic equations.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
32 (2000)
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
Maurizio Badii, "Existence and uniqueness of periodic solutions for a quasilinear parabolic problem", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 32 (2000), pp. 123-138.
Languages
en
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