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

Journal of the European Mathematical Society (2004)

- Volume: 006, Issue: 2, page 193-205
- ISSN: 1435-9855

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topGalaktionov, 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 -

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