Comparison of Some Solution Concepts for Linear First-order Hyperbolic Differential Equations With Non-smooth Coefficients
Simon Haller, Günther Hörmann (2008)
Publications de l'Institut Mathématique
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Displaying similar documents to “Well-posedness of the Cauchy problem for hyperbolic equations with non-Lipschitz coefficients.”
Comparison of Some Solution Concepts for Linear First-order Hyperbolic Differential Equations With Non-smooth Coefficients
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New general unique solvability conditions of the Cauchy problem for systems of general linear functional differential equations are established. The class of equations considered covers, in particular, linear equations with transformed argument, integro-differential equations, neutral type equations and their systems of an arbitrary order.
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Regularity and uniqueness in quasilinear parabolic systems
Pavel Krejčí, Lucia Panizzi (2011)
Applications of Mathematics
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Inspired by a problem in steel metallurgy, we prove the existence, regularity, uniqueness, and continuous data dependence of solutions to a coupled parabolic system in a smooth bounded 3D domain, with nonlinear and nonhomogeneous boundary conditions. The nonlinear coupling takes place in the diffusion coefficient. The proofs are based on anisotropic estimates in tangential and normal directions, and on a refined variant of the Gronwall lemma.