English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

This paper deals with a general system of equations and conditions arisingfrom a mathematical model of prostate cancer growth with chemotherapy andantiangiogenic therapy that has been recently introduced and analyzed (see [P.Colli et al., Mathematical analysis and simulation study of a phase-field modelof prostate cancer growth with chemotherapy and antiangiogenic therapy effects,Math. Models Methods Appl. Sci. 30 (2020), 1253-1295], preprint inarXiv:1907.11618 [math.AP]). The related system includes two evolutionaryoperator equations involving fractional powers of selfadjoint, nonnegative,unbounded linear operators having compact resolvents. Both equations containnonlinearities and in particular the equation describing the dynamics of thetumor phase variable has the structure of a Allen-Cahn equation withdouble-well potential and additional nonlinearity depending also on the othervariable, which represents the nutrient concentration. The equation for thenutrient concentration is nonlinear as well, with a term coupling bothvariables. For this system we design an existence, uniqueness and continuousdependence theory by setting up a careful analysis which allows theconsideration of nonsmooth potentials and the treatment of continuousnonlinearities with general growth properties.

Well-posedness for a class of phase-field systems modeling prostate cancer growth with fractional operators and general nonlinearities