(untitled) (Journal of Partial Differential Equations, 2020)
In this paper we study the first boundary value problem for nonlinear diffusion equation &#8706u&#8706t + &#8706&#8706xf(u) = &#8706&#8706xA(&#8706&#8706xB(u)) whereA(s) = &#8747&sup1_0a(&#963)d&#963, B(s) = &#8747&sup1_0b(&#963)d&#963 with a(s) &#8805 0, b(s) &#8805 0. We prove the existence of BV solutions under the much general structural conditions lim_s &#8594 + &#8734 A(s) = +&#8734, lim_s &#8594 - &#8734 A(s) = -&#8734 Moreover, we show the uniqueness without any structural conditions.