We now apply thermodynamic principles to field theories with memory. For general
nonlinear, nonisothermal theories, we assume that a free energy is given, this being the …

We study the numerical solution of an initial-boundary value problem for a Volterra type
integro-differential equation, in which the integral operator is a convolution product of a …

Non-linear singular integral equations are investigated in connection with some basic
applications in two-dimensional fluid mechanics. A general existence and uniqueness …

This book is Part II of a two-volume work on inequalities. It concentrates on one-and
multidimensional nonlinear integral and discrete Gronwall-Bellman-type inequalities and …

This paper studies finite-element approximations to the solutions of the nonlinear diffusion
equations with memory. An elliptic projection with memory associated with our equations is …

We study the nonlinear Volterra equation (1) u′(t)+ Bu (t)+ a∗ Au (t)+ d dt (b∗ u (t))= F (t),
t≥ 0, u (0)= u 0. https://s3-euw1-ap-pe-df-pch-content-public-p. s3. eu-west-1. amazonaws …

Page 1 BIRKHÄUSER Operator Theory Advances and Applications Vol. 184 Nonlinear
Parabolic-Hyperbolic Coupled Systems and Their Attractors Yuming Qin APDE Advances in …

In the last decade, considerable interest has been generated in the study of classes of ill-
posed problems for partial differential equations and integrodifferential equations, with …

It is well known that inequalities are a very important tool in classical analysis. One
application of these inequalities is the theory of PDEs (Partial Differential Equations). To our …

The equation (*)\quadu_tt(x,t)=ϕ(u_x(x,t)_x-\int_0^tm(t-τ)ψ(u_x(x,τ))_xdτ+f(x,t),\quadx∈B⊂R
,\quadt≧0, provides a model for the motion of a one-dimensional viscoelastic body. Here …