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Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model

1Meng Fan is partially supported by NSFC-11271065, RFPD-20130043110001, and RFCPCMSP-2014

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  • This paper studies the global existence and uniqueness of classicalsolutions for a generalized quasilinear parabolic equation withappropriate initial and mixed boundary conditions. Under somepracticable regularity criteria on diffusion item and nonlinearity, weestablish the local existence and uniqueness of classical solutionsbased on a contraction mapping. This local solution can be continuedfor all positive time by employing the methods of energy estimates, $ L^{p} $-theory, and Schauder estimate of linear parabolic equations. Astraightforward application of global existence result of classical solutions to a density-dependent diffusion model of in vitroglioblastoma growth is also presented.

    Mathematics Subject Classification: Primary: 35A01, 35A02, 35A09; Second: 92B05.

    Citation:

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