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On the First Boundary Value Problem for Quasilinear Parabolic Equations with Two Independent Variables

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Abstract

This paper is concerned with the global solvability of the first initial boundary value problem for the quasilinear parabolic equations with two independent variables: a(t, x, u, u x)u xx - u t = f (t, x, u, u x). We investigate the case when the growth of \(\frac{{\left| {f(t,x,u,p)} \right|}}{{a(t,x,u,p)}}\) with respect to p is faster than p 2 when |p| → ∞. Conditions which guarantee the global classical solvability of the problem are formulated.

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Authors and Affiliations

  1. Department of Mathematics, University of Crete, 71409, Heraklion - Crete, Greece

    Alkis S. Tersenov

  2. Lavrentyev Institute of Hydrodynamics, Novosibirsk, Russia

    Alkis S. Tersenov

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  1. Alkis S. Tersenov
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Tersenov, A.S. On the First Boundary Value Problem for Quasilinear Parabolic Equations with Two Independent Variables. Arch. Rational Mech. Anal. 152, 81–92 (2000). https://doi.org/10.1007/s002050000074

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