This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra
integral equations (VIEs), ranging from Volterra's fundamental contributions and the …

Pavol Quittner Philippe Souplet Blow-up, Global Existence and Steady States Second
Edition Page 1 Birkhäuser Advanced Texts Basler Lehrbücher Pavol Quittner Philippe …

Using a different and much shorter approach, we prove a blow-up result which is more
general than the interesting blow-up result of G. Todorova and B. Yordanov concerning a …

There is an enormous amount of work in the literature about the blow-up behavior of
evolution equations. It is our intention to introduce the theory by emphasizing the methods …

We prove that solutions to the critical wave equation (1.1) with dimension n⩾ 4 can not be
global if the initial values are positive somewhere and nonnegative. This completes the …

В предлагаемой книге излагается общий подход к априорным оценкам решений
нелинейных уравнений и неравенств в частных производных, основанный на методе …

The parabolic partial differential equations model one of the most important processes in the
real-world: diffusion. Whether it is the diffusion of energy in space-time, the diffusion of …

This paper is concerned with establishing necessary or sufficient conditions for the existence
of solutions to evolution equations with fractional derivatives in space and time. The Fujita …

This paper concerns with the Cauchy problems of semilinear pseudo-parabolic equations.
After establishing the necessary existence, uniqueness and comparison principle for mild …

Boundary control of nonlinear parabolic PDEs is an open problem with applications that
include fluids, thermal, chemically-reacting, and plasma systems. In this paper we present …