Work

Approximation of the Solutions to Quasilinear Parabolic Problems with Perturbed $$VMO_x$$ Coefficients

Year: 2025

Type: article

Abstract: We consider the Cauchy-Dirichlet problem for second-order quasilinear operators of parabolic type in non-divergence form. The data are Carathéodory functions, and the principal part is of $$VMO_x$$ V M O x -type with respect to the variables ( x , t ). Assuming the existence of a strong solution $$u_0,$$ u 0 , we apply the Implicit Function Theorem in a neighbourhood of this solution to show that small bounded perturbations of the data lead to small perturbations of the solution $$u_0$$ u 0 itself. Furthermore, we employ the Newton iteration procedure to construct an approximating sequence that converges to $$u_0$$ u 0 in the corresponding Sobolev space.

Source: Nonlinear Differential Equations and Applications NoDEA

DOI: 10.1007/s00030-025-01174-z

Authors: Rosamaria Rescigno, Lubomira G. Softova

Institution: University of Salerno

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Ministero dell’Istruzione, dell’Università e della Ricerca, Akademie Věd České Republiky, Università degli Studi di Salerno