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