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- W1966617243 abstract "We prove existence results for the initial-boundary value problem for parabolic equations of the type $$left{ {begin{array}{*{20}c} {u_t + A(u) + g(x,t,u{mathbf{ }})|nabla u|^2 = f{mathbf{ }}in{mathbf{ }}Omega times (0,{mathbf{ }}T),} {u = 0{mathbf{ }}on{mathbf{ }}partial Omega times (0,{mathbf{ }}T),} {u(x,{mathbf{ }}0) = u_0 (x){mathbf{ }}in{mathbf{ }}Omega ,} end{array} } right.$$ where ω is a bounded open subset ofR N and T>0, A is a pseudomonotone operator of Leray-Lions type defined in L2(), T; H 0 1 (ω), u0 is in L1 (ω) and g(x, t, s) is only assumed to be a Carathéodory function satisfying a sign condition. The result is achieved by proving the strong convergence in L2 (0, T; H 0 1 (ω)) of trucations of solutions of approximating problems with L1 converging data. To underline the importance of this tool, we show how it can be used for getting other existence theorems, dealing in particular with the following class of Cauchy-Dirichlet problems: $$left{ {begin{array}{*{20}c} {u_t + A(u) = f{mathbf{ }} + div{mathbf{ }}(Phi (u))in{mathbf{ }}Omega times (0,{mathbf{ }}T),} {u = 0{mathbf{ }}on{mathbf{ }}partial Omega times (0,{mathbf{ }}T),} {u(x,{mathbf{ }}0) = u_0 (x){mathbf{ }}in{mathbf{ }}Omega ,} end{array} } right.$$ where ΦεC0 (R, R N) and the data f and u0 are still taken in L1(Q) and L1(ω) respectively." @default.
- W1966617243 created "2016-06-24" @default.
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- W1966617243 date "1999-12-01" @default.
- W1966617243 modified "2023-10-05" @default.
- W1966617243 title "Existence results for nonlinear parabolic equations via strong convergence of truncations" @default.
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- W1966617243 doi "https://doi.org/10.1007/bf02505907" @default.
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