Samarsky A . A. , Galactions V. A. , Kurdyumov S. P. , Mikhailov A. P. Exacerbation modes in problems for quasilinear parabolic equations. The article considers the solutions (regimes with exacerbation) of quasilinear parabolic equations that describe the processes of heat conduction and combustion in continuous nonlinear media that are unlimitedly growing in a finite time; the main attention is paid to the effect of heat localization. The conditions for the emergence of unlimited solutions have been established and their asymptotic behavior has been studied .. Special methods for the study of nonlinear parabolic equations are presented, properties of difference schemes for individual classes of equations. are studied. The problems of the book are closely related to a wide range of topical problems of physics, biophysics, chemistry, biology, which are now intensively studied within the theory of dissipative structures and synergetics. For specialists in the field of nonlinear equations of mathematical physics, applied mathematics, as well as students and postgraduates of relevant specialties .