# Uniform analytic-Gevrey regularity of solutions to a semilinear heat equation

Todor Gramchev; Grzegorz Łysik

Banach Center Publications (2008)

- Volume: 81, Issue: 1, page 213-226
- ISSN: 0137-6934

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topTodor Gramchev, and Grzegorz Łysik. "Uniform analytic-Gevrey regularity of solutions to a semilinear heat equation." Banach Center Publications 81.1 (2008): 213-226. <http://eudml.org/doc/282415>.

@article{TodorGramchev2008,

abstract = {We study the Gevrey regularity down to t = 0 of solutions to the initial value problem for a semilinear heat equation $∂_tu - Δu = u^M$. The approach is based on suitable iterative fixed point methods in $L^p$ based Banach spaces with anisotropic Gevrey norms with respect to the time and the space variables. We also construct explicit solutions uniformly analytic in t ≥ 0 and x ∈ ℝⁿ for some conservative nonlinear terms with symmetries.},

author = {Todor Gramchev, Grzegorz Łysik},

journal = {Banach Center Publications},

keywords = {semilinear heat equation; initial value problem; anisotropic Gevrey spaces},

language = {eng},

number = {1},

pages = {213-226},

title = {Uniform analytic-Gevrey regularity of solutions to a semilinear heat equation},

url = {http://eudml.org/doc/282415},

volume = {81},

year = {2008},

}

TY - JOUR

AU - Todor Gramchev

AU - Grzegorz Łysik

TI - Uniform analytic-Gevrey regularity of solutions to a semilinear heat equation

JO - Banach Center Publications

PY - 2008

VL - 81

IS - 1

SP - 213

EP - 226

AB - We study the Gevrey regularity down to t = 0 of solutions to the initial value problem for a semilinear heat equation $∂_tu - Δu = u^M$. The approach is based on suitable iterative fixed point methods in $L^p$ based Banach spaces with anisotropic Gevrey norms with respect to the time and the space variables. We also construct explicit solutions uniformly analytic in t ≥ 0 and x ∈ ℝⁿ for some conservative nonlinear terms with symmetries.

LA - eng

KW - semilinear heat equation; initial value problem; anisotropic Gevrey spaces

UR - http://eudml.org/doc/282415

ER -

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