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On a novel gradient flow structure for the aggregation equation
The aggregation equation arises naturally in kinetic theory in the study of granular media, and its interpretation as a 2-Wasserstein gradient flow...
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Ill-posedness for the Half wave Schrödinger equation
We study the Cauchy problem for the half wave Schrödinger equation introduced by Xu [
9 ]. There are some well-posedness results for the equation,... -
An Application of the Simplest Equations Method to Logarithmic Schrödinger Equation
In this paper we apply the Simple Equations Method (SEsM) to obtain exact solution of equations which are connected to the nonlinear logarithmic...
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Lump solutions of the fractional Kadomtsev–Petviashvili equation
Of concern is the fractional Kadomtsev–Petviashvili (fKP) equation and its lump solution. As in the classical Kadomtsev–Petviashvili equation, the...
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Very Weak Solution of the Wave Equation for Sturm-Liouville Operator
We considered the initial-boundary value problem for the wave equation with the Sturm-Liouville operator with singular coefficients. The method of...
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The Quasispecies Equation
In this chapter, we first introduce the general quasispecies equation.We then present the classical Perron–Frobenius theorem and apply it to solve...
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On the Exact Global Controllability of a Semilinear Evolution Equation
AbstractFor the Cauchy problem associated with a controlled semilinear evolution equation with an operator (not necessarily bounded) in a Hilbert...
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Explicit Solutions of the Nonlinear Schrödinger-Type Equation
In this work, we focus on the construction of explicit solutions of the nonlinear Schrödinger-type equation, which has various applications in...
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The periodic solution of a second order linear equation
This paper deals with a class of second-order linear differential equations with periodic coefficients. By viable transformation, we put the...
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Stochastic Clairaut Equation on Algebra of Generalized Functions
Based on an infinite dimensional distributions space, we study the solution of the generalized stochastic Clairaut equation using a suitable...
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Simulation of Domain Walls: Simple Waves in the Magnetodynamics Equation
AbstractA partial differential equation modeling the motion of a domain wall taking into account external magnetic fields and dam** is considered....
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Stability of a generalized Euler–Lagrange radical multifarious functional equation
In this paper, we introduce a new generalized version of the Euler–Lagrange functional equation, namely, generalized Euler–Lagrange radical...
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On a Boundary Value Problem for a Pseudohyperbolic Equation
AbstractIn the present article, we consider a mixed boundary value problem in a quarter-space for a pseudohyperbolic equation. We find conditions on...
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Orbital Stability of Solitary Wave for Eckhaus–Kundu Equation
In this paper, the orbital stability of solitary wave for Eckhaus–Kundu equation is studied. Since the equation we studied is difficult to be...
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Three-Level Scheme for Solving the Radiation Diffusion Equation
AbstractA method for the numerical solution of a nonlinear equation describing the diffusion transfer of radiation energy has been developed....
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The Mixed Initial-Boundary Value Problem for Degenerate Hyperbolic Equation
A new class of initial-boundary value problems with nonlocal conditions on the Newton potential for the case of a degenerate equation were set and...
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Asymptotic Solutions of Burgers Equation and Modified Burgers Equation Satisfying Flux Type Conditions
In this article, we solve exactly an initial boundary value problem (IBVP) for Burgers equation satisfying flux type conditions using Cole-Hopf...
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A Novel Spectral Method for the Subdiffusion Equation
In this paper, we design and analyze a novel spectral method for the subdiffusion equation. As it has been known, the solutions of this equation are...