Related papers: A note on the nonlinear derived Cauchy problem
For the Cauchy problem for an operator differential equation of the form $y'(z) = Ay(z)$, where $A$ is a closed linear operator on a Banach space over the completion of an algebraic closure of the field of $p$-adic numbers, a criterion of…
We study the Cauchy problem for fully nonlinear (stochastic) parabolic partial differential equations. We provide both in deterministic and stochastic case the existence of a maximal defined solution for the problem and we provide suitable…
We construct a sequence that converges to a solution of the Cauchy problem for a singularly perturbed linear inhomogeneous differential equation of an arbitrary order. This sequence is also an asymptotic sequence in the following sense: the…
We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on…
In this paper we consider the Schr{\"o}dinger equation with nonlinear derivative term. Our goal is to initiate the study of this equation with non vanishing boundary conditions. We obtain the local well posedness for the Cauchy problem on…
In this paper, we deal with a Cauchy problem for a nonlinear fractional differential equation with the Caputo derivative of order $\alpha \in (0, 1)$. As initial data, we consider a pair consisting of an initial point, which does not…
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…
We prove the persistence of analyticity for classical solution of the Cauchy problem for quasilinear wave equations with analytic data. Our results show that the analyticity of solutions, stated by the Cauchy-Kowalewski and…
We construct a sheaf theoretic and derived geometric machinery to study nonlinear partial differential equations and their singular supports. We establish a notion of derived microlocalization for solution spaces of non-linear equations and…
We study the problem of existence, uniqueness and regularity of probabilistic solutions of the Cauchy problem for nonlinear stochastic partial differential equations involving operators corresponding to regular (nonsymmetric) Dirichlet…
In this paper, we study the Cauchy problem for a nonlinear wave equation with frictional and viscoelastic damping terms. Our aim is to obtain the threshold, to classify the global existence of solution for small data or the finite time…
This paper studies global solvability of the Cauchy problem for a generalized time-fractional Kuramoto-Sivashinsky equation in the Shwartz space, which is a complete topological space generated by a family of semi-norms. The main approach…
We study an infinite system of ordinary differential equations that models the evolution of coagulating and fragmenting clusters, which we assume to be composed of identical units. Under very mild assumptions on the coefficients we prove…
To study the existence and uniqueness of solutions to Cauchy-type problems for fractional q-difference equations with the bi-ordinal Hilfer fractional q-derivative which is an extension of the Hilfer fractional q-derivative. An approach is…
We consider the Cauchy problem for a second-order nonlinear evolution equation in a Hilbert space. This equation represents the abstract generalization of the Ball integro-differential equation. The general nonlinear case with respect to…
In this paper we study the Cauchy problem for overdetermined systems of linear partial differential operators with constant coefficients in some spaces of $\omega$-ultradifferentiable functions in the sense of Braun, Meise and Taylor, for…
Using the continuous limit approximation in the dynamical system we study a nonlinear partial differential equation which corresponds to the generalization of both the Fermi-Pasta-Ulam and the Frenkel-Kontorova models. This generalized…
Parabolic integro-differential nondegenerate Cauchy problem is considered in the scale of L_{p} spaces of functions whose regularity is defined by a Levy measure with O-regulary varying radial profile. Existence and uniqueness of a solution…
We consider the Cauchy problem associated with a general parabolic partial differential equation in $d$ dimensions. We find a family of closed-form asymptotic approximations for the unique classical solution of this equation as well as…
This paper studies the properties of solutions for a double nonlinear time-dependent parabolic equation with variable density, not in divergence form with a source or absorption. The problem is formulated as a partial differential equation…