Quasilinear Cauchy-Dirichlet problem for parabolic equations with VMOx coefficients

Authors

  • Rosamaria Rescigno University of Salerno, 132, Via Giovanni Paolo II, Fisciano, 84084 (SA), Italy

DOI:

https://doi.org/10.21638/spbu01.2025.109

Abstract

We study the strong solvability of the Cauchy-Dirichlet problem for parabolic quasilinear equations with discontinuous data. The principal coefficients depend on the point (x, t) and on the solution u, the dependence on x is of VMO type while these are only measurable with respect to t. Assuming suitable structural conditions on the nonlinear terms, we prove existence and uniqueness of the strong solution, which turns out to be also Holder continuous.

Keywords:

quasilinear parabolic equations, Cauchy-Dirichlet problem, VMOx coefficients, fixed point theorem, strong solutions

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Published

2025-05-14

How to Cite

Rescigno, R. (2025). Quasilinear Cauchy-Dirichlet problem for parabolic equations with VMOx coefficients. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 12(1), 117–128. https://doi.org/10.21638/spbu01.2025.109

Issue

Vol. 12 No. 1 (2025)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.