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Sur l’équation de la corrosion intergranulaire par diffusion de surface. (On the equation of intergranular corrosion by surface diffusion). (French) Zbl 0623.65133
We prove an existence-uniqueness result for the solution of a nonlinear fourth-order differential equation which determines the shape of a grain boundary groove forming by surface diffusion. A variational approximation of the problem leads to an efficient numerical method.
MSC:
65Z05 Applications to the sciences
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
80A32 Chemically reacting flows
65H10 Numerical computation of solutions to systems of equations
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