INDEX action, 115, 163, 519 activator, 175 adjoint, 448, 726 bilinear form, 322 of elliptic operator, 322 admissible states, 633 Airy’s equation, 4, 178 almost everywhere (a.e.), 733 almost separably valued function, 737 amplitude and phase, 219 analyticity, 238–245 of harmonic functions, 31 of solutions to heat equation, 62 power series, 241–245 antigradient flux function, 657 a priori estimates, 541 Arzela–Ascoli compactness criterion, 291, 479, 582, 721 asymptotics, 156, 211–233 averages, 702 B¨ acklund transformation, 696 backwards uniqueness heat equation, 63 Banach space, 257, 264, 722 Barenblatt–Kompaneetz–Zeldovich solution, 186 barrier, 369 basis of eigenfunctions, 170, 357, 377, 383, 386, 388, 411, 413, 414, 531 orthonormal, 724 beam equation, 4, 450 Bernoulli’s law, 209 Bessel potential, 192 biharmonic equation, 368 bilinear form, 316 estimates for, 319–321 time-dependent, 375, 401, 426 bistable equation, 180 blow-up conservation law, 641 nonlinear heat equation, 550, 551 nonlinear wave equation, 676, 688–693 porous medium equation, 171 reaction diffusion equation, 540 Bochner’s Theorem, 737 bootstrap argument, 489 boundary, 712 analytic, 712 Ck, 712 normal to, 713 straightening, 102, 236, 240, 339, 345, 713 boundary-value problem eigenvalue problem, 356 homogenization of, 230 Laplace’s equation, 40 nonlinear boundary conditions, 524 nonlinear eigenvalue problem, 491 nonlinear Poisson equation, 545, 557 Poisson’s equation, 27, 41 quasilinear elliptic equation, 529, 543 second-order elliptic equation, 313, 316 745

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