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The surface diffusion flow with elasticity in the plane. (English) Zbl 1458.35406

Summary: In this paper we prove short-time existence of a smooth solution in the plane to the surface diffusion equation with an elastic term and without an additional curvature regularization. We also prove the asymptotic stability of strictly stable stationary sets.

MSC:

35Q74 PDEs in connection with mechanics of deformable solids
35B65 Smoothness and regularity of solutions to PDEs
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
74K35 Thin films
74G65 Energy minimization in equilibrium problems in solid mechanics
74N25 Transformations involving diffusion in solids
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References:

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