Journal
EUROPEAN JOURNAL OF APPLIED MATHEMATICS
Volume -, Issue -, Pages -Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0956792522000134
Keywords
Singular elliptic equation; van der Waals force; Thin film
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We study the steady states of the fourth-order thin-film equation with van der Waals force in a bounded domain, considering the mass constraint. This leads to a singular elliptic equation for the thickness with an unknown pressure term. By analyzing a second-order nonlinear ordinary differential equation, we prove the existence of infinitely many radially symmetric solutions. Additionally, we perform rigorous asymptotic analysis to identify the blow-up limit when the steady state is close to a constant solution and the blow-down limit when the maximum of the steady state goes to infinity.
We consider steady states with mass constraint of the fourth-order thin-film equation with van der Waals force in a bounded domain which leads to a singular elliptic equation for the thickness with an unknown pressure term. By studying second-order nonlinear ordinary differential equation, h(rr) + 1/2 h(r) = 1/alpha h(-alpha) - p we prove the existence of infinitely many radially symmetric solutions. Also, we perform rigorous asymptotic analysis to identify the blow-up limit when the steady state is close to a constant solution and the blow-down limit when the maximum of the steady state goes to the infinity.
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