Nonlinear Parabolic Operators with Perturbed Coefficients

Lutz Recke, Lubomira Softova

Abstract


We consider the Cauchy-Dirichlet problem for second order quasilinear non-divergence form parabolic equations  with discontinuous data in a bounded cylinder \(Q\). Supposing  existence of strong solution \(u_0\) and applying the Implicit Function Theorem we show that for any  small \(L^\infty\)-perturbation of the coefficients there exists, locally in time, exactly one solution \(u\) close to $u_0$ with respect to the norm in \(W^{2,1}_p(Q)\) which depends smoothly on the data. For that, no structure and growth conditions on the data are needed. Moreover, applying the  Newton Iteration Procedure we obtain an approximating sequence for the solution \(u_0\).

Keywords


Nonlinear parabolic equations; Cauchy-Dirichlet problem; VMO; Implicit Function Theorem; Newton Iteration Procedure

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References


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DOI: http://dx.doi.org/10.26713%2Fcma.v9i3.790

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