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This article is cited in 9 scientific papers (total in 9 papers)
On the Absence of Local Solutions of Several Evolutionary Problems
E. I. Galakhov Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
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.
Received: 27.10.2008
Citation:
E. I. Galakhov, “On the Absence of Local Solutions of Several Evolutionary Problems”, Mat. Zametki, 86:3 (2009), 337–349; Math. Notes, 86:3 (2009), 314–324
Linking options:
https://www.mathnet.ru/eng/mzm8498https://doi.org/10.4213/mzm8498 https://www.mathnet.ru/eng/mzm/v86/i3/p337
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Abstract page: | 408 | Full-text PDF : | 189 | References: | 56 | First page: | 16 |
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