On higher-order semilinear parabolic equations with measures as initial data

Galaktionov, Victor. "On higher-order semilinear parabolic equations with measures as initial data." Journal of the European Mathematical Society 006.2 (2004): 193-205. <http://eudml.org/doc/277209>.

@article{Galaktionov2004,
abstract = {We consider $2m$th-order $(m\ge 2)$ semilinear parabolic equations $u_t=−(−\Delta )^mu\pm |u|^\{p−1\}u$ in $\mathcal \{R\}^N\times \mathbb \{R\}_+$$(p>1)$, with Dirac’s mass $\delta (x)$ as the initial function. We show that for $p<p_0=1+2m/N$, the Cauchy problem admits a solution $u(x,t)$ which is bounded and smooth for small $t>0$, while for $p\ge p_0$ such a local in time solution does not exist. This leads to a boundary layer phenomenon in constructing a proper solution via regular approximations.},
author = {Galaktionov, Victor},
journal = {Journal of the European Mathematical Society},
keywords = {semilinear parabolic equations; Cauchy problem; boundary layer phenomenon; regular approximations; Dirac mass; existence; nonexistence; boundary layer phenomenon; regular approximations; Dirac mass; existence; nonexistence},
language = {eng},
number = {2},
pages = {193-205},
publisher = {European Mathematical Society Publishing House},
title = {On higher-order semilinear parabolic equations with measures as initial data},
url = {http://eudml.org/doc/277209},
volume = {006},
year = {2004},
}

TY - JOUR
AU - Galaktionov, Victor
TI - On higher-order semilinear parabolic equations with measures as initial data
JO - Journal of the European Mathematical Society
PY - 2004
PB - European Mathematical Society Publishing House
VL - 006
IS - 2
SP - 193
EP - 205
AB - We consider $2m$th-order $(m\ge 2)$ semilinear parabolic equations $u_t=−(−\Delta )^mu\pm |u|^{p−1}u$ in $\mathcal {R}^N\times \mathbb {R}_+$$(p>1)$, with Dirac’s mass $\delta (x)$ as the initial function. We show that for $p<p_0=1+2m/N$, the Cauchy problem admits a solution $u(x,t)$ which is bounded and smooth for small $t>0$, while for $p\ge p_0$ such a local in time solution does not exist. This leads to a boundary layer phenomenon in constructing a proper solution via regular approximations.
LA - eng
KW - semilinear parabolic equations; Cauchy problem; boundary layer phenomenon; regular approximations; Dirac mass; existence; nonexistence; boundary layer phenomenon; regular approximations; Dirac mass; existence; nonexistence
UR - http://eudml.org/doc/277209
ER -