We prove the existence of weak solutions for the strongly nonlinear parabolic problem
in the anisotropic Sobolev space , where the data f are assumed to be in the dual, and the nonlinear term g(x, t, s) has growth and sign conditions on s.
We prove an existence result of a nonlinear parabolic equation under Dirichlet null boundary conditions in Sobolev spaces of infinite order, where the second member belongs to 1 ( ).
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