Annali di Matematica Pura ed Applicata

, Volume 87, Issue 1, pp 375–388 | Cite as

On the existence of a generalized solution to the first initial-boundary value problem for a nonlinear parabolic equation

  • V. Šeda
Article
  • 16 Downloads

Summary

In the paper first the existence of a classical solution to an initial-boundary value problem for the nonlinear parabolic equation\(\frac{{\partial z}}{{\partial t}} = \frac{{\partial ^2 z}}{{\partial x^2 }} + f\left( {x,t,z} \right)\) is proved under the standard condition on Hölder continuity of f but a quite general condition on the growth of f. Then, by using the possibility of the approximation of a continuous function by means of Hölder continuous functions, the foregoing result is applied to the proof of the existence of a generalized solution to the first boundary value problem for the same equation where only continuity of f and a weak assumption on the growth of f is required.

Keywords

Continuous Function General Condition Standard Condition Generalize Solution Parabolic Equation 

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Copyright information

© Nicola Zanichelli Editore 1970

Authors and Affiliations

  • V. Šeda
    • 1
  1. 1.BratislavaCzechoslovakia

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