Geodesic
Evolution equations with monotone operator and functional non-linearity at the time derivative
Sbornik. Mathematics, Tome 191 (2000) no. 9, pp. 1301-1322

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Conditions for the solubility of the so-called doubly non-linear equations $$ Au+\frac\partial{\partial t}Bu=f, \qquad u(0)=u_0, $$ are investigated. Here $A$ is a monotone operator induced by a differential expression containing higher-order partial derivatives and $B$ is an operator induced by a monotone function. A theorem on the existence of a solution is proved. The method of monotone operators is used in combination with the method of compact operators. Examples of applications to parabolic differential equations are presented. 
@article{SM_2000_191_9_a2,
     author = {G. I. Laptev},
     title = {Evolution equations with monotone operator and functional non-linearity at the time derivative},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
     volume = {191},
     number = {9},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_9_a2/}
}
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G. I. Laptev. Evolution equations with monotone operator and functional non-linearity at the time derivative. Sbornik. Mathematics, Tome 191 (2000) no. 9, pp. 1301-1322. http://geodesic.mathdoc.fr/item/SM_2000_191_9_a2/