Geodesic
On the Absence of Local Solutions of Several Evolutionary Problems
Matematičeskie zametki, Tome 86 (2009) no. 3, pp. 337-349.

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We consider the existence problem for local (with respect to time) solutions of quasilinear evolutionary partial differential equations and inequalities with singular coefficients and initial conditions. We obtain sufficient conditions for instantaneous blow-up of solutions and show that the results thus obtained cannot be improved in the function class under study.
Keywords: existence problem, quasilinear evolutionary PDE, weak solution, Dirichlet boundary condition, heat equation, Sobolev space, Carathéodory function. 
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E. I. Galakhov. On the Absence of Local Solutions of Several Evolutionary Problems. Matematičeskie zametki, Tome 86 (2009) no. 3, pp. 337-349. http://geodesic.mathdoc.fr/item/MZM_2009_86_3_a2/

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