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A parabolic quasilinear problem for linear growth functionals. (English) Zbl 1010.35063

The authors prove an existence and uniqueness result for a nonlinear nonhomogeneous parabolic problem in divergence form by assuming that the energy functional has linear growth. The asymptotic behavior of solutions is also discussed. As particular cases, they consider the time-dependent minimal surface equation and the evolution problem for plastic antiplanar shear.
Reviewer: Ioan Vrabie (Iasi)

MSC:

35K65 Degenerate parabolic equations
47H20 Semigroups of nonlinear operators
35K55 Nonlinear parabolic equations
47H06 Nonlinear accretive operators, dissipative operators, etc.
35B45 A priori estimates in context of PDEs
35B50 Maximum principles in context of PDEs
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References:

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