Abstract
AbstractIn this content, we investigate a class of fractional parabolic equation with general nonlinearities $$\begin{aligned} \frac{\partial z(x,t)}{\partial t}-(\Delta +\lambda )^{\frac{\beta }{2}}z(x,t)=a(x_{1})f(z), \end{aligned}$$
∂
z
(
x
,
t
)
∂
t
-
(
Δ
+
λ
)
β
2
z
(
x
,
t
)
=
a
(
x
1
)
f
(
z
)
,
where a and f are nondecreasing functions. We first prove that the monotone increasing property of the positive solutions in $$x_{1}$$
x
1
direction. Based on this, nonexistence of the solutions are obtained by using a contradiction argument. We believe these new ideas we introduced will be applied to solve more fractional parabolic problems.
Funder
Agencia Estatal de Investigación
Publisher
Springer Science and Business Media LLC
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