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- W54418267 abstract "We begin this chapter with some general results on the existence and regularity of solutions to semilinear parabolic PDE, first treating the pure initial-value problem in § 1, for PDE of the form 0.1 $$frac{partial u} {partial t} = Lu + F(t,x,u,nabla u),quad u(0) = f,$$ where u is defined on [0, T) × M, and M has no boundary. Some of the results established in § 1 will be useful in the next chapter, on nonlinear, hyperbolic equations. We also give a precursor to results on the global existence of weak solutions, which will be examined further in Chap. 17, in the context of the Navier–Stokes equations for fluids." @default.
- W54418267 created "2016-06-24" @default.
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- W54418267 date "2010-10-27" @default.
- W54418267 modified "2023-09-25" @default.
- W54418267 title "Nonlinear Parabolic Equations" @default.
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- W54418267 doi "https://doi.org/10.1007/978-1-4419-7049-7_3" @default.
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