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

100%

Gramchev T., Łysik G.

Banach Center Publications

2008

tom 81

nr 1

213-226

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.

Propagation of uniform Gevrey regularity of solutions to evolution equations

100%

Gramchev T., Wang Y.-G.

Banach Center Publications

2003

tom 60

nr 1

279-293

We investigate the propagation of the uniform spatial Gevrey $G^σ$, σ ≥ 1, regularity for t → +∞ of solutions to evolution equations like generalizations of the Euler equation and the semilinear Schrödinger equation with polynomial nonlinearities. The proofs are based on direct iterative arguments and nonlinear Gevrey estimates.

Ograniczanie wyników

2 Banach Center Publications

2 Gramchev T.

1 Wang Y.-G.

1 Łysik G.

1 2008

1 2003

Wyniki wyszukiwania

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

Propagation of uniform Gevrey regularity of solutions to evolution equations