Faedo-Galerkin Approximations for nonlinear Heat equation on Hilbert Manifold

 Hussain, Javed

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In this work, we aim to study the well-posedness of a deterministic problem consisting of the non-linear heat equation of gradient type. The evolution equation emerges by projecting the Laplace operator with Dirichlet boundary conditions and polynomial nonlinearity of degree 2n-1, onto the tangent space of the sphere \mathcal{M} in a Hilbert space \mathcal{H}. We are going to deal with the question of existence and uniqueness based on the Faedo-Galerkin compactness method.


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 Hussain, Javed