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1.
We show that any entropy solution u of a convection diffusion equation ?t u + div F(u)-Df(u) = b{\partial_t u + {\rm div} F(u)-\Delta\phi(u) =b} in Ω × (0, T) belongs to C([0,T),L1loc(W)){C([0,T),L^1_{\rm loc}({\Omega}))} . The proof does not use the uniqueness of the solution. 相似文献
2.
In this paper we study the existence of a solution in ${L^\infty_{\rm loc}(\Omega)}In this paper we study the existence of a solution in L¥loc(W){L^\infty_{\rm loc}(\Omega)} to the Euler–Lagrange equation for the variational problem
inf[`(u)] + W1,¥0(W) òW (ID(?u) + g(u)) dx, (0.1)\inf_{\bar u + W^{1,\infty}_0(\Omega)} \int\limits_{\Omega} ({\bf I}_D(\nabla u) + g(u)) dx,\quad \quad \quad \quad \quad(0.1) 相似文献
3.
Marino Badiale Lorenzo Pisani Sergio Rolando 《NoDEA : Nonlinear Differential Equations and Applications》2011,18(4):369-405
We study the sum of weighted Lebesgue spaces, by considering an abstract measure space (W,A,m){(\Omega ,\mathcal{A},\mu)} and investigating the main properties of both the Banach space
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