Geodesic
A Time Regularity Result for Forward-Backward Parabolic Equations
Bollettino della Unione matematica italiana, Série 9, Tome 4 (2011) no. 1, pp. 69-77.

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We give a time regularity result for an abstract mixed type equation whose toy model may be $(ru)_t - \Delta u = f$ where $r$ is a coefficient whose sign may be positive, null and negative. 
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     title = {A {Time} {Regularity} {Result} for {Forward-Backward} {Parabolic} {Equations}},
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Paronetto, Fabio. A Time Regularity Result for Forward-Backward Parabolic Equations. Bollettino della Unione matematica italiana, Série 9, Tome 4 (2011) no. 1, pp. 69-77. http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_1_a3/

[1] F. Paronetto, G-convergence of mixed type evolution operators, J. Math. Pures Appl. (9) 93 (2010), no. 4, 361-407. | DOI | MR | Zbl

[2] F. Paronetto, Existence results for a class of evolution equations of mixed type, J. Funct. Anal., 212 (2) (2004), 324-356. | DOI | MR | Zbl