Classical solutions to quasilinear parabolic problems with dynamic boundary conditions

Davide  Guidetti

doi:10.3934/dcdss.2016024

Article Contents

2016, Volume 9, Issue 3: 717-736. Doi: 10.3934/dcdss.2016024

This issue Previous Article Generalized Wentzell boundary conditions for second order operators with interior degeneracy Next Article Inverse problems for evolution equations with time dependent operator-coefficients

Classical solutions to quasilinear parabolic problems with dynamic boundary conditions

Davide Guidetti^1,

1.
Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna

Received: November 2014

Published: June 2016

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Abstract

We study linear nonautonomous parabolic systems with dynamic boundary conditions. Next, we apply these results to show a theorem of local existence and uniqueness of a classical solution to a second order quasilinear system with nonlinear dynamic boundary conditions.

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Mathematics Subject Classification: Primary: 35K55; Secondary: 35K15.

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References

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