Related papers: Variational resolution for some general classes of…
We prove the existence of global solutions for some coupled systems of partially nonautonomous evolution inclusions comprised of a Cauchy problem with a compact resolvent semigroup generator and an evolution equation governed by a…
We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal $L_p$-regularity in time-weighted function spaces. It is shown that our notion of…
We obtain the well-posedness and Schauder estimates for a class of system of linear, quasi-linear and non-linear second order partial differential equations. We deduce existence and uniqueness of a global smooth solution of a non-linear and…
We prove that evolution families on complex complete hyperbolic manifolds are in one to one correspondence with certain semicomplete non-autonomous holomorphic vector fields, providing the solution to a very general Loewner type…
We prove the existence and uniqueness of solutions for a family of nonlinear parabolic systems related to phase field models taking in account variations of temperature and the possibility of a general class of nonlinearities. The present…
Averaging principle for abstract non-autonomous parabolic evolution equations governed by time-dependent family of positive sectorial operators is proved. Apart from linear case also a nonlinear version for continuous perturbations is…
We expand our group classification of quasilinear evolution equations (Acta Appl.Math., v.69, 2001) to the case of general evolution equation in one spatial variable. This enables obtaining several new classes of evolution equations with…
We present a family of integral equation-based solvers for the heat equation, reaction-diffusion systems, the unsteady Stokes equation and the incompressible Navier-Stokes equations in two space dimensions. Our emphasis is on the…
The connection of the 'time' evolution of the eigenstates of the reflectionless potentials of the Lax hierarchy to the more general case of the 'time' evolution of the eigenstates of the Schroedinger equation for potentials with…
This note is devoted to a small, but essential, extension of Theorem 2.1 of our recent paper [6]. The improvement is explained in Section 1 and proved in Section 2. The importance of the extension is demonstrated in Section 3 with an…
We show existence and uniqueness results for nonlinear parabolic equations in noncylindrical domains with possible jumps in the time variable
We provide a novel existence result for energy-variational solutions to a general class of evolutionary partial differential equations. Compared to previous works on this solution concept, the generalization is mainly twofold: a relaxation…
We carry out an analysis of the existence of solutions for a class of nonlinear partial differential equations of parabolic type. The equation is associated to a nonlocal initial condition, written in general form which includes, as…
We prove unique continuation principles for solutions of evolution Schr\"odinger equations with time dependent potentials. These correspond to uncertainly principles of Paley-Wiener type for the Fourier transform. Our results extends to a…
In this article, we provide existence results for a general class of nonlocal and nonlinear second-order parabolic equations. The main motivation comes from front propagation theory in the cases when the normal velocity depends on the…
We present analytical results and numerical simulations for a class of nonlinear dispersive equations in two spatial dimensions. These equations are of (derivative) nonlinear Schr\"odinger type and have recently been obtained in \cite{DLS}…
Here we study the abstract nonlinear differential equation of second order that in special case is the equation of the type of equation of traffic flow. We prove the solvability theorem for the posed problem under the appropriate conditions…
We consider a Cauchy Dirichlet problem for a quasilinear second order parabolic equation with lower order term driven by a singular coefficient. We establish an existence result to such a problem and we describe the time behavior of the…
This second part deals with applications of a general method to describe the quantum time evolution determined by a Schroedinger equation with time-dependent Hamiltonian. A new aspect of our approach is that we find all solutions starting…
In this work, we are concerned with existence of solutions for a nonlinear second-order distributional differential equation, which contains measure differential equations and stochastic differential equations as special cases. The proof is…