On quasilinear parabolic evolution equations in weighted $L_p$-spaces TeX Export

@article{citeulike:5779499, abstract = {In this paper we develop a geometric theory for quasilinear parabolic problems in weighted \$L\_p\$-spaces. We prove existence and uniqueness of solutions as well as the continuous dependence on the initial data. Moreover, we make use of a regularization effect for quasilinear parabolic equations to study the \$\om\$-limit sets and the long-time behaviour of the solutions. These techniques are applied to a free boundary value problem. The results in this paper are mainly based on maximal regularity tools in (weighted) \$L\_p\$-spaces.}, archivePrefix = {arXiv}, author = {Koehne, Matthias and Pruess, Jan and Wilke, Mathias}, citeulike-article-id = {5779499}, citeulike-linkout-0 = {http://arxiv.org/abs/0909.1480}, citeulike-linkout-1 = {http://arxiv.org/pdf/0909.1480}, day = {8}, eprint = {0909.1480}, keywords = {equations, evolution, l\_p, parabolic, quasilinear, weighted}, month = {Sep}, posted-at = {2009-09-13 19:56:17}, priority = {2}, title = {On quasilinear parabolic evolution equations in weighted \$L\_p\$-spaces}, url = {http://arxiv.org/abs/0909.1480}, year = {2009} }

TY - JOUR ID - citeulike:5779499 L3 - citeulike-article-id:5779499 N2 - In this paper we develop a geometric theory for quasilinear parabolic problems in weighted $L_p$-spaces. We prove existence and uniqueness of solutions as well as the continuous dependence on the initial data. Moreover, we make use of a regularization effect for quasilinear parabolic equations to study the $\om$-limit sets and the long-time behaviour of the solutions. These techniques are applied to a free boundary value problem. The results in this paper are mainly based on maximal regularity tools in (weighted) $L_p$-spaces. TI - On quasilinear parabolic evolution equations in weighted $L_p$-spaces KW - equations KW - evolution KW - l_p KW - parabolic KW - quasilinear KW - weighted AU - Koehne, Matthias AU - Pruess, Jan AU - Wilke, Mathias PY - 2009/Sep/08/ UR - http://arxiv.org/abs/0909.1480 ER -