%0 Conference Proceedings %T Existence and Uniqueness of Blow-up Solutions for a Parabolic Problem with a Localized Nonlinear Term via Semi-group Theory %+ Department of Mathematics %+ Modélisation Mathématique en Mécanique (M3) %+ Department of Mathematics %+ Department of Mathematics %A Sawangtong, Panumart %A Licht, Christian %A Novaprateep, Boriboon %A Orankitjaroen, Somsak %< avec comité de lecture %( East-West Journal of Mathematics %B International Conference on Mathematics and Applications, ICMA-MU 2009 %C Thailand %P 139-152 %8 2009-12-18 %D 2009 %K semilinear parabolic problems %K blow-up %K semigroups of linear operator %Z Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph] %Z Physics [physics]/Mechanics [physics]/Materials and structures in mechanics [physics.class-ph] %Z Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of materials [physics.class-ph] %Z Physics [physics]/Mechanics [physics]/Mechanics of materials [physics.class-ph] %Z Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph] %Z Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph] %Z Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph] %Z Physics [physics]/Mechanics [physics]/Structural mechanics [physics.class-ph]Conference papers %X Here, we use the semigroup theory to establish the existence, uniqueness and blow-up for a classical solution of a semilinear parabolic problem with localized nonlinear term| a locally Lipschitz continuous function of the value of the solution at a point of a 1-dimensional domain. Our method, which uses Sobolev spaces and fractional power of operators, is in contrast with the classical ones (Green functions) which supply similar results in 1-dimensional settings. %G English %2 https://hal.science/hal-00747045/document %2 https://hal.science/hal-00747045/file/Existence_uniqueness_Sawangtong_al.pdf %L hal-00747045 %U https://hal.science/hal-00747045 %~ CNRS %~ LMGC %~ MIPS %~ UNIV-MONTPELLIER %~ UM-2015-2021