Carleman Estimate for Elliptic Operators with Coefficients with Jumps at an Interface in Arbitrary Dimension and Application to the Null Controllability of Linear Parabolic Equations

We analyze the linear theory of parabolic equations in uniform spaces. We obtain sharp Lp-Lq-type estimates in uniform spaces for heat and Schrödinger semigroups and analyze the regularizing effect and the exponential type of these semigroups. We also deal with general second-order elliptic operators and study the generation of analytic semigoups in uniform spaces.

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Asymptotic behavior of solutions for linear parabolic equations with general measure data

Comptes Rendus Mathematique ◽

10.1016/j.crma.2007.03.021 ◽

2007 ◽

Vol 344 (9) ◽

pp. 571-576 ◽

Cited By ~ 19

Author(s):

Francesco Petitta

Keyword(s):

Asymptotic Behavior ◽

Parabolic Equations ◽

Measure Data ◽

Asymptotic Behavior Of Solutions ◽

General Measure ◽

Linear Parabolic Equations

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Second order linear parabolic equations in uniform spaces in $${\varvec{\mathbb {R}^{N}}}$$ R N

Revista Matemática Complutense ◽

10.1007/s13163-016-0215-0 ◽

2016 ◽

Vol 30 (1) ◽

pp. 63-78

Author(s):

Carlos Quesada ◽

Aníbal Rodríguez-Bernal

Keyword(s):

Parabolic Equations ◽

Second Order ◽

Uniform Spaces ◽

Order Linear ◽

Linear Parabolic Equations

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Grid approximation of singularly perturbed boundary value problem for quasi-linear parabolic equations in the case of complete degeneracy in spatial variables

Russian Journal of Numerical Analysis and Mathematical Modelling ◽

10.1515/rnam.1991.6.3.243 ◽

1991 ◽

Vol 6 (3) ◽

Cited By ~ 5

Author(s):

G. I. SHISHKIN

Keyword(s):

Boundary Value Problem ◽

Parabolic Equations ◽

Boundary Value ◽

Singularly Perturbed ◽

Spatial Variables ◽

Grid Approximation ◽

Linear Parabolic Equations

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Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/ijmms.2005.523 ◽

2005 ◽

Vol 2005 (4) ◽

pp. 523-536

Author(s):

Yubin Yan

Keyword(s):

Difference Method ◽

Parabolic Equations ◽

Parabolic Problem ◽

Approximation Scheme ◽

Time Derivative ◽

Nonsmooth Data ◽

Smoothing Property ◽

Linear Parabolic Equations ◽

Linear Parabolic Problem ◽

Data Error

A smoothing property in multistep backward difference method for a linear parabolic problem in Hilbert space has been proved, where the operator is selfadjoint, positive definite with compact inverse. By using the solutions computed by a multistep backward difference method for the parabolic problem, we introduce an approximation scheme for time derivative. The nonsmooth data error estimate for the approximation of time derivative has been obtained.

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