
Resumo: We present a semilinear mathematical model for thermal conduction problems defined on one-dimensional moving boundary domains, known in the literature as moving boundary problems or problems on non-cylindrical domains. We prove the existence and finite fractal dimension of the pullback attractors on tempered universes. Regarding the finiteness of the fractal dimension of the pullback attractor, we apply the method of Lyapunov exponents, associated with uniformly differentiable processes defined on families of Hilbert spaces that are parametrized in time.
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