We prove existence and uniqueness of solutions for a class of forward-backward diffusion equations via a representative example, where the second-order part has continuous spectrum, and the initial and boundary data are suitably chosen.
AARAO, JORGE (2005) "Forward-Backward Diffusion With Continuous Spectrum," Turkish Journal of Mathematics: Vol. 29: No. 1, Article 3. Available at: https://journals.tubitak.gov.tr/math/vol29/iss1/3