# Gevrey well posedness for $3$-evolution equations with variable coefficients

@inproceedings{Junior2021GevreyWP, title={Gevrey well posedness for \$3\$-evolution equations with variable coefficients}, author={Alexandre Arias Junior and A. Ascanelli and M. Cappiello}, year={2021} }

We study the Cauchy problem for a class of third order linear anisotropic evolution equations with complex valued lower order terms depending both on time and space variables. Under suitable decay assumptions for |x| → ∞ on these coefficients, we prove a well posedness result in Gevrey-type spaces. 2010 Mathematics Subject Classification: 35G10, 35S05, 35B65, 46F05

#### One Citation

The Cauchy problem for $3$-evolution equations with data in Gelfand-Shilov spaces

- Mathematics
- 2020

We consider the Cauchy problem for a $3$-evolution operator $P$ with complex valued lower order terms. We assume the initial data to be Gevrey regular and to admit an exponential decay at infinity… Expand

#### References

SHOWING 1-10 OF 30 REFERENCES

Well-posedness of the Cauchy problem for p-evolution equations

- Mathematics
- 2012

Abstract We consider p-evolution equations in ( t , x ) with real characteristics. We give sufficient conditions for the well-posedness of the Cauchy problem in Sobolev spaces, in terms of decay… Expand

Semilinear p-evolution equations in Sobolev spaces

- Mathematics
- 2016

Abstract 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… Expand

THE CAUCHY PROBLEM FOR p-EVOLUTION EQUATIONS

- Mathematics
- 2010

In this paper we deal with the Cauchy problem for evolution equations with real characteristics. We show that the problem is well-posed in Sobolev spaces assuming a suitable decay of the coefficients… Expand

Gevrey Regularity of the Global Attractor for Damped Forced KdV Equation on the Real Line

- Psychology
- 2018

We consider here a weakly damped KdV equation on the real line with forcing term that belongs to some Gevrey space. We prove that the global attractor is also contained into such a space of analytic… Expand

Pseudodifferential parametrices of infinite order for SG-hyperbolic problems.

- Mathematics
- 2003

In this paper we consider a class of symbols of infinite order and develop a global calculus for the related pseudodifferential operators in the functional frame of the Gelfand-Shilov spaces of type… Expand

Schrödinger-type equations in Gelfand-Shilov spaces

- Mathematics
- 2018

We study the initial value problem for Schr\"odinger-type equations with initial data presenting a certain Gevrey regularity and an exponential behavior at infinity. We assume the lower order terms… Expand

On the Cauchy Problem for the Generalized Korteweg-de Vries Equation

- Mathematics
- 2003

Abstract We consider the local and global Cauchy problem for the generalized Korteweg-de Vries equation , with initial data in homogeneous and nonhomogeneous Besov spaces. This allows us to slightly… Expand

Anisotropic Gevrey regularity for mKdV on the circle

- Mathematics
- 2011

It is shown that the solution to the Cauchy problem for the modifi ed Korteweg-de Vries equation with initial data in an analytic Gevrey space $G^\sigma$, $\sigma \>= 1$, as a function of the… Expand

Linear Partial Differential Operators in Gevrey Spaces

- Mathematics
- 1993

Differential operators with constant coefficients Gevrey pseudo-differential operators of infinite order canonical transformations and classical analytic Fourier integral operators propagation of… Expand

Well-posedness for degenerate Schrödinger equations

- Physics
- 2014

We consider the initial value problem for Schrodinger type equations
$$\frac{1}{i}\partial_tu-a(t)\Delta_xu+\sum_{j=1}^nb_j(t,x)\partial_{x_j}u=0$$
with $a(t)$ vanishing of finite order at $t=0$… Expand