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- W2073755315 abstract "In the paper first the existence of a classical solution to an initial-boundary value problem for the nonlinear parabolic equation $$frac{{partial z}}{{partial t}} = frac{{partial ^2 z}}{{partial x^2 }} + fleft( {x,t,z} right)$$ 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." @default.
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- W2073755315 title "On the existence of a generalized solution to the first initial-boundary value problem for a nonlinear parabolic equation" @default.
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- W2073755315 doi "https://doi.org/10.1007/bf02411988" @default.
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