We prove in this paper an existence result of entropy solutions for nonlinear parabolic equations of the form:

$$\begin{aligned} \displaystyle \frac{\partial u}{\partial t}-{\text {div}}\, a(x,t,u,\nabla u)-\mathrm{div}\Phi (x,t,u)= f \quad \text {in }{Q_T=\Omega \times (0,T)}, \end{aligned}$$

where the lower order term \(\Phi \) satisfies only a natural growth condition prescribed by the N-function M defining the Orlicz spaces framework and the data f are an element of \(L^1(Q_T)\). We do not assume any restriction neither on M nor on its complementary \(\overline{M}\). No particular growth is considered on \(\Phi \).

中文翻译：

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非自反Orlicz空间中具有非标准增长的非线性抛物方程的熵解

我们在本文中证明以下形式的非线性抛物方程的熵解的存在结果：

$$ \ begin {aligned} \ displaystyle \ frac {\ partial u} {\ partial t}-{\ text {div}} \，a（x，t，u，\ nabla u）-\ mathrm {div} \ hi（x，t，u）= f \ quad \ text {in} {Q_T = \ Omega \ times（0，T）}，\ end {aligned} $$

其中低阶项\（\ Phi \）仅满足由定义Orlicz空间框架的N函数M规定的自然增长条件，并且数据f是\（L ^ 1（Q_T）\）的元素。我们既不对M也不对其补充\（\ overline {M} \）施加任何限制。\（\ Phi \）上没有考虑任何特定的增长。