Classical solutions to a moving boundary problem for an elliptic-parabolic system | Zendy

Joachim Escher | Zendy

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Classical solutions to a moving boundary problem for an elliptic-parabolic system

Author(s) -

Joachim Escher

Publication year - 2004

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/96

Subject(s) - boundary value problem , homogeneous , mathematical analysis , parabolic partial differential equation , mathematics , boundary (topology) , class (philosophy) , free boundary problem , boundary problem , computer science , partial differential equation , combinatorics , artificial intelligence

In this paper we investigate a simple model describing in vivo cancer growth for a single tumor. The model comprises a reaction-diffusion equation describing the evolution of the nutrient concentration, denoted by u, and an elliptic equation for the internal pressure, denoted by p, in the tissue. The cell proliferation rate is denoted by f(u), wheref : R ! R is assumed to be smooth. Typically, this proliferation rate f is assumed to be linear or of logistic type (cf. [6, p. 157] and [7, pp. 190, 193]). A polynomial proliferation rate is proposed in the Appendix of [16]. At time t the tumor occupies the domain(t) with the moving boundary(t) . In dimensionless formp and u satisfy the equations

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