Abstract
Abstract In this paper, we provide existence and uniqueness of entropy solutions to a general nonlinear parabolic problem on a general convex set with merely integrable data and in the setting of Orlicz spaces.
Highlights
When trying to generalize the last condition of a(., ξ ) to the non polynomial one, we are led to replace the space Lp(0, T; W 1,p(Ω)) by an inhomogeneous Sobolev space W 1,xLM built from an Orlicz space LM instead of Lp, where the N -function M, which defines LM, defines the new growth of the operator
Our purpose in this paper is to prove existence results and uniqueness, of the entropy solution, of the problem (P) in the setting of the inhomogeneous Sobolev space W 1,xLM with data f ∈ L1(Q)
Let us recall that two equivalent N -functions defined the same Orlicz space
Summary
When trying to generalize the last condition of a(., ξ ) to the non polynomial one, we are led to replace the space Lp(0, T; W 1,p(Ω)) by an inhomogeneous Sobolev space W 1,xLM built from an Orlicz space LM instead of Lp, where the N -function M, which defines LM, defines the new growth of the operator. Our purpose in this paper is to prove existence results and uniqueness, of the entropy solution, of the problem (P) in the setting of the inhomogeneous Sobolev space W 1,xLM with data f ∈ L1(Q). In these types of problems the proofs are essentially based on the good choice of the test functions.
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