TY - JOUR AU - Recke, Lutz AU - Softova, Lubomira PY - 2018/09/25 Y2 - 2024/03/29 TI - Nonlinear Parabolic Operators with Perturbed Coefficients JF - Communications in Mathematics and Applications JA - Comm. Math. Appl. VL - 9 IS - 3 SE - Research Article DO - 10.26713/cma.v9i3.790 UR - http://www.rgnpublications.com/journals/index.php/cma/article/view/790 SP - 277 - 292 AB - 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 \(u_0\). ER -