Abstract
In this chapter, we present some results on global existence and uniqueness of solutions to evolutionary PEDs obtained by application of analytic inequalities in Chapters 1 and 2. This chapter consists of four sections. In Section 4.1, we use the simultaneous singular Bellman–Gronwall inequality, i.e., Theorem 1.3.2, to discuss the local existence, regularity, and continuous dependence on initial data of solutions to a weakly coupled parabolic system for non-regular initial data. In Section 4.2, we use Theorem 1.4.9 to study some properties of solutions to the Cauchy problem for multi-dimensional conservation laws with anomalous diffusion. In Section 4.3, we use Theorem 2.1.19 to investigate the blow-up of solutions of semilinear heat equations.
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Qin, Y. (2017). Global Existence and Uniqueness for Evolutionary PDEs. In: Analytic Inequalities and Their Applications in PDEs. Operator Theory: Advances and Applications(), vol 241. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-00831-8_4
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DOI: https://doi.org/10.1007/978-3-319-00831-8_4
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-00830-1
Online ISBN: 978-3-319-00831-8
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