On a Class of Quasilinear Parabolic Equations of Second Order with Double-degeneracy (Journal of Partial Differential Equations, 2020)
In this paper we study the first boundary value problem for nonlinear diffusion equation \frac{&#8706u}{&#8706t} + \frac{&#8706}{&#8706x}f(u) = \frac{&#8706}{&#8706x}A(\frac{&#8706}{&#8706x}B(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.