Related papers: On the Time Derivative in a Quasilinear Equation
We prove local in time well-posedness in Sobolev spaces of the Cauchy problem for semi-linear p-evolution equations of the first order with real principal part, but complex valued coefficients for the lower order terms, assuming decay…
We consider two evolution equations involving space fractional Laplace operator of order $0<s<1$. We first establish some existence and uniqueness results for the considered evolution equations. Next, we give some comparison theorems and…
Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…
We study an evolutionary $p$-Laplace problem whose potential is subject to a translation in time. Provided the trajectory along which the potential is translated admits a sufficiently regular local time, we establish existence of solutions…
Some results on nonexistence of nontrivial solutions to some time and space fractional differential evolution equations with transformed space argument are obtained via the nonlinear capacity method. The analysis is then used for a $2\times…
The set of integrable symmetries of the nonstationary Schr\"{o}dinger equation is shown to admit a natural decomposition into subsets of mutually commuting symmetries. Hierarchies of time evolutions associated with each of these subsets…
A closed expression for the harmonic oscillator wave function after the passage of a linear signal with arbitrary time dependence is derived. Transition probabilities are simple to express in terms of Laguerre polynomials. Spontaneous…
The purpose of this paper is to investigate the time behavior of the solution of a weighted $p$-Laplacian evolution equation, given by \begin{align} \label{eveq} \begin{cases} u_{t} = \text{div} \left(\gamma |\nabla u|^{p-2}\nabla u \right)…
We prove that every local derivation on a complex semisimple finite-dimensional Leibniz algebra is a derivation.
In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on Banach space with locally monotone operators, which is a generalization of the classical result by J.L. Lions for monotone operators.…
For weak solutions to the evolutional $p$-Laplace equation with a time-dependent Radon measure on the right hand side we obtain pointwise estimates via a nonlinear parabolic potential.
We prove existence of solution to a nonlinear first-order nabla dynamic equation on an arbitrary bounded time scale with boundary conditions, where the right-hand side of the dynamic equation is a continuous function.
We examine the short and long-time behaviors of time-fractional diffusion equations with variable space-dependent order. More precisely, we describe the time-evolution of the solution to these equations as the time parameter goes either to…
In this paper, we construct the transport equation and the wave equation with specular derivatives and solve these equations in one-dimension. To solve these equations, we introduce new function spaces, which we term specular spaces,…
In this paper we derive the Schroedinger equation by assuming it describes the time evolution of a deterministic and reversible process that leaves at each moment in time a different observable well defined; that is, it allows an accurate…
Our study of abstract quasi-linear parabolic problems in time-weighted L_p-spaces, begun in [17], is extended in this paper to include singular lower order terms, while keeping low initial regularity. The results are applied to…
A four dimensional treatment of nonrelativistic space-time gives a natural frame to deal with objective time derivatives. In this framework some well known objective time derivatives of continuum mechanics appear as Lie-derivatives. Their…
The global existence of weak solutions to a class of quasilinear parabolic equations with nonlinearities depending on first order terms and integrable data in a moving domain is investigated. The class includes the $p$-Laplace equation as a…
We study existence, uniqueness, norm estimates and asymptotic time behaviour (in some cases can be claimed to be sharp) for the solution of a general evolutionary integral (differential) equation of scalar type on a locally compact…
This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of…