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Rothe time-discretization method for a nonlinear parabolic p(u) -Laplacian problem with Fourier-type boundary condition and $$L^1$$-data

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In this paper, we prove the existence and uniqueness results of entropy solutions to a class of nonlinear parabolic p(u)-Laplacian problem with Fourier-type boundary conditions and $$L^1$$ -data. The main… Click to show full abstract

In this paper, we prove the existence and uniqueness results of entropy solutions to a class of nonlinear parabolic p(u)-Laplacian problem with Fourier-type boundary conditions and $$L^1$$ -data. The main tool used here is the Rothe method combined with the theory of variable exponent Sobolev spaces.

Keywords: fourier type; problem fourier; type boundary; nonlinear parabolic; parabolic laplacian; laplacian problem

Journal Title: Ricerche Di Matematica
Year Published: 2020

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