Chapter
§1.5 Local theorems of existence and continuous dependence on initial data in the Hölder classes of weight functions
pp.：
53 – 58
2 Construction of Liapunov’s functionals in the case of one spatial variable
pp.：
58 – 71
§2.2 The existence condition for Liapunov’s functionals
pp.：
71 – 81
§2.1 Liapunov’s functionals of the first order
pp.：
71 – 71
§2.3 A priori estimates of the first derivative
pp.：
81 – 88
§2.4 Some generalization of the Liapunov functionals concept
pp.：
88 – 96
§2.5 Liapunov functionals of the second order
pp.：
96 – 106
§2.6 A priori estimates of the second derivative
pp.：
106 – 112
§2.7 Liapunov functionals in the neighborhood of a dynamic problem solution
pp.：
112 – 119
3 The behavior of solutions of one-dimensional nonlinear problems over extended time
pp.：
119 – 131
§3.1 Liapunov’s functionals and asymptotic behavior of solutions for extended time
pp.：
131 – 132
§3.2 The discrete Liapunov functional
pp.：
132 – 154
§3.3 Qualitative properties of mixed problem solutions for nonlinear parabolic equations
pp.：
154 – 161
§3.4 Some examples
pp.：
161 – 197
§3.5 Some qualitative properties of dissipative boundary-value problems for quasilinear parabolic equations with one spatial variable
pp.：
197 – 209
4 The stability criterion for the trivial solution to the mixed problem for the second order parabolic equation
pp.：
209 – 217
§4.1 The stability criterion for the trivial solution to the linear problem
pp.：
217 – 219
§4.2 The stability criterion of the trivial solution of the linear mixed problem for the second order parabolic equation with time coefficients that are periodic in time
pp.：
219 – 237
§4.3 Justification of the linearization method for the bounded nonstationary solution of the parabolic equation
pp.：
237 – 242
§4.4 Stable solution of the Neumann problem
pp.：
242 – 247
5 The attraction domains of stable stationary or stable periodic solutions
pp.：
247 – 253
§5.1 Some definitions and the preliminary results
pp.：
253 – 254
§5.2 The greatest and least periodic solutions of the mixed problem
pp.：
254 – 265
§5.3 The attraction domains of a stable periodic solution
pp.：
265 – 282
§5.4 The classification of periodic solutions
pp.：
282 – 295
§5.5 Solutions, periodic in time, of the mixed problems for autonomous parabolic equations
pp.：
295 – 302
6 On stabilization of mixed problem solutions for autonomous quasilinear parabolic equations
pp.：
302 – 309
§6.1 Setting of the problem and preliminary results
pp.：
309 – 310
§6.2 Stable ω-limit sets of solutions of the autonomous quasilinear parabolic equation
pp.：
310 – 317
§6.3 Unstable ω-limit sets of solutions for the autonomous quasilinear parabolic equation
pp.：
317 – 324
§6.4 Stabilization of solutions of boundary-value problems and monotone solutions of boundary-value problems
pp.：
324 – 336
§A.2 The basic estimates
pp.：
353 – 356
§A.1 Setting of the problem
pp.：
353 – 353
§A.3 Proof of theorem 2.1
pp.：
356 – 359
§A.4 Estimate for the polynomial function
pp.：
359 – 360
§A.5 Estimate for the case μ ≠ 0
pp.：
360 – 362
§A.6 Setting of the model problem. Some solution estimates
pp.：
362 – 370
§A.7 The general theorem on the estimate for solution derivative for the mixed problem
pp.：
370 – 375
§A.8 The uniform by the regularization parameters derivative estimate for the model problem and its corollaries
pp.：
375 – 381
§A.9 The existence theorems for the model and basic problems. The uniqueness condition
pp.：
381 – 387
Bibliography
pp.：
387 – 395
Qualitative Theory of Parabolic Equations, Part 1
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