If I is an open bounded interval and T>0, the initial-boundary-value problem
(EP)⎧⎩⎨⎪⎪b(u)t−a(u,φ(u)x)x=fb(u)=v0u=0in Q=]0,T[×I,on {0}×Ion Γ=]0,T[×∂I

is under consideration, where a:(z,ξ)∈ℝ×ℝ→ℝ is continuous, nondecreasing in ξ∈ℝ with a(0,0)=0; b:ℝ→ℝ is continuous, nondecreasing and surjective with b(0)=0; and φ:ℝ→ℝ is continuous, nondecreasing with φ(0)=0. Existence of entropy solutions is proved for nondecreasing continuous functions b and φ vanishing at zero; and for a continuous function a vanishing at zero and nondecreasing with respect to second variable, under the structure condition of H. W. Alt and S.Luckhaus

initial-boundary-value problem; homogeneous Dirichlet conditions