On parabolic equations in one space dimension

N. V. Krylov

doi:10.1080/03605302.2015.1126734

On parabolic equations in one space dimension

N. V. Krylov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Several negative results are presented concerning the solvability in Sobolev classes of the Cauchy problem for the inhomogeneous second-order uniformly parabolic equations without lower order terms in one space dimension. The main coefficient is assumed to be a bounded measurable function of (t, x) bounded away from 0. We also discuss upper and lower estimates of certain kind on the fundamental solutions of such equations.

Original language	English (US)
Pages (from-to)	644-664
Number of pages	21
Journal	Communications in Partial Differential Equations
Volume	41
Issue number	4
DOIs	https://doi.org/10.1080/03605302.2015.1126734
State	Published - Mar 17 2015

Bibliographical note

Publisher Copyright:
© 2016 Taylor & Francis.

Keywords

Absence of a priori estimates
Estimates on the fundamental solutions
Sobolev classes

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10.1080/03605302.2015.1126734

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abstract = "Several negative results are presented concerning the solvability in Sobolev classes of the Cauchy problem for the inhomogeneous second-order uniformly parabolic equations without lower order terms in one space dimension. The main coefficient is assumed to be a bounded measurable function of (t, x) bounded away from 0. We also discuss upper and lower estimates of certain kind on the fundamental solutions of such equations.",

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AB - Several negative results are presented concerning the solvability in Sobolev classes of the Cauchy problem for the inhomogeneous second-order uniformly parabolic equations without lower order terms in one space dimension. The main coefficient is assumed to be a bounded measurable function of (t, x) bounded away from 0. We also discuss upper and lower estimates of certain kind on the fundamental solutions of such equations.

KW - Absence of a priori estimates

KW - Estimates on the fundamental solutions

KW - Sobolev classes

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JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 4

ER -

On parabolic equations in one space dimension

Abstract

Bibliographical note

Keywords

Publisher link

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