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A Noncharacteristic Cauchy Problem for Linear Parabolic Equations I: Solvability

✍ Scribed by Dinh Nho Haò

Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
944 KB
Volume
171
Category
Article
ISSN
0025-584X

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✦ Synopsis

Noncharacteristic Cauchy problems for parabolic equations are frequently encountered in many areas of heat transfer. These problems are well known to be severely ill-posed. In this paper a solvability criterion for a class of such problems is established. It is proved that a weak solution of a noncharacteristic Cauchy problem for linear parabolic equations in divergence form with coefficients in a Holmgren class 2 in time exists if and only if the Cauchy data are functions of a Holmgren class 2! A function g ( t ) defined on (a, 8) is said to be of a Holmgren class 2, if g E Cm(a, b) and for all nonnegative integers n there exist positive constants c and s such that 1g'"'1 < cs"(2n)!.

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A Remark on the Global Solvability of the Cauchy Problem for Quasilinear Parabolic Equations
✍ Aris S. Tersenov 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 81 KB

The present paper is concerned with the global solvability of the Cauchy problem for the quasilinear parabolic equations with two independent variables: Ž . Ž . u s a t, x, u, u u q f t, x, u, u . We investigate the case of the arbitrary order < < of growth of the function f t, x, u, p with respect