## Nonlinear Partial Differential Equations with ApplicationsThis book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality. |

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### Contents

III | 1 |

IV | 3 |

V | 6 |

VI | 7 |

VII | 8 |

IX | 9 |

X | 10 |

XI | 14 |

LVI | 175 |

LVII | 178 |

LVIII | 185 |

LIX | 187 |

LX | 190 |

LXI | 193 |

LXII | 199 |

LXIII | 201 |

XII | 19 |

XIII | 20 |

XIV | 22 |

XV | 25 |

XVI | 27 |

XVII | 29 |

XVIII | 33 |

XIX | 35 |

XX | 40 |

XXI | 41 |

XXII | 42 |

XXIII | 46 |

XXIV | 53 |

XXV | 56 |

XXVI | 58 |

XXVII | 59 |

XXVIII | 62 |

XXIX | 69 |

XXX | 79 |

XXXI | 86 |

XXXII | 89 |

XXXIII | 93 |

XXXV | 95 |

XXXVI | 99 |

XXXVII | 102 |

XXXVIII | 103 |

XXXIX | 106 |

XL | 107 |

XLI | 109 |

XLII | 114 |

XLIII | 120 |

XLIV | 124 |

XLV | 125 |

XLVI | 129 |

XLVII | 135 |

XLVIII | 144 |

XLIX | 152 |

LI | 156 |

LII | 159 |

LIII | 161 |

LIV | 168 |

LV | 172 |

LXIV | 215 |

LXV | 221 |

LXVI | 228 |

LXVII | 232 |

LXVIII | 239 |

LXIX | 242 |

LXXI | 244 |

LXXII | 252 |

LXXIII | 255 |

LXXIV | 257 |

LXXV | 262 |

LXXVI | 267 |

LXXVII | 272 |

LXXVIII | 275 |

LXXIX | 280 |

LXXX | 286 |

LXXXI | 291 |

LXXXII | 295 |

LXXXIII | 302 |

LXXXIV | 305 |

LXXXV | 309 |

LXXXVI | 313 |

LXXXVII | 318 |

LXXXVIII | 321 |

XCI | 327 |

XCII | 332 |

XCIII | 334 |

XCIV | 335 |

XCV | 339 |

XCVI | 341 |

XCVII | 342 |

XCVIII | 351 |

XCIX | 355 |

C | 357 |

CI | 361 |

CII | 365 |

CIII | 368 |

CIV | 372 |

CV | 376 |

383 | |

399 | |

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### Common terms and phrases

a-priori estimates A(uk accretive approximation assume assumption Aubin-Lions Banach space boundary conditions boundary-value problem bounded boundedness Brezis Caratheodory mapping coercive compact embedding consider convergence d-monotone defined denote dense derivative differential equations Dirichlet Dirichlet boundary conditions dom(A dom(L elliptic Example Exercise existence follows Galerkin method Green's formula Gronwall inequality Gronwall's growth condition hence Hilbert holds implies interpolation Jn Jr Lebesgue Lemma liminf limit passage limsup linear Lipschitz continuous locally convex space lower semicontinuous LP(I m-accretive Math modify monotone Moreover Necas Nemytskii mapping nonlinear norm Note obtain parabolic particular potential Proposition prove pseudomonotone radially continuous realize reflexive Remark resp satisfy semilinear seminorm sequence set-valued so-called Sobolev space Springer strong solution subsequence term uniformly convex unique variational inequality weak formulation weak solution weakly continuous weakly lower Zeidler 354

### Popular passages

Page 383 - Implications of viscosity and strain-gradient effects for the kinetics of propagating phase boundaries in solids, manuscript in preparation.

Page 383 - AMANN, H., QUITTNER, P.: Elliptic boundary value problems involving measures: existence, regularity, and multiplicity. Adv. Differ. Equ. 3 (1998), 753-813.

### References to this book

Self-dual Partial Differential Systems and Their Variational Principles Nassif Ghoussoub Limited preview - 2008 |

Viability, Invariance and Applications Ovidiu Carja,Mihai Necula,Ioan I. Vrabie Limited preview - 2007 |