On the solution of the heat equation with nonlinear unbounded memory

Doktor, Alexander. "On the solution of the heat equation with nonlinear unbounded memory." Aplikace matematiky 30.6 (1985): 461-474. <http://eudml.org/doc/15428>.

@article{Doktor1985,
abstract = {The paper deals with the question of global solution $u,\tau $ to boundary value problem for the system of semilinear heat equation for $u$ and complementary nonlinear differential equation for $\tau $ (“thermal memory”). Uniqueness of the solution is shown and the method of successive approximations is used for the proof of existence of a global solution provided the condition $(\mathcal \{P\})$ holds. The condition $(\mathcal \{P\})$ is verified for some particular cases (e. g.: bounded nonlinearity, homogeneous Neumann problem (even for unbounded nonlinearities), apriori estimate of the solution holds).},
author = {Doktor, Alexander},
journal = {Aplikace matematiky},
keywords = {heat equation; nonlinear unbounded memory; uniqueness; existence; boundary value problem; heat equation; nonlinear unbounded memory; uniqueness; existence; boundary value problem},
language = {eng},
number = {6},
pages = {461-474},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the solution of the heat equation with nonlinear unbounded memory},
url = {http://eudml.org/doc/15428},
volume = {30},
year = {1985},
}

TY - JOUR
AU - Doktor, Alexander
TI - On the solution of the heat equation with nonlinear unbounded memory
JO - Aplikace matematiky
PY - 1985
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 30
IS - 6
SP - 461
EP - 474
AB - The paper deals with the question of global solution $u,\tau $ to boundary value problem for the system of semilinear heat equation for $u$ and complementary nonlinear differential equation for $\tau $ (“thermal memory”). Uniqueness of the solution is shown and the method of successive approximations is used for the proof of existence of a global solution provided the condition $(\mathcal {P})$ holds. The condition $(\mathcal {P})$ is verified for some particular cases (e. g.: bounded nonlinearity, homogeneous Neumann problem (even for unbounded nonlinearities), apriori estimate of the solution holds).
LA - eng
KW - heat equation; nonlinear unbounded memory; uniqueness; existence; boundary value problem; heat equation; nonlinear unbounded memory; uniqueness; existence; boundary value problem
UR - http://eudml.org/doc/15428
ER -